What are rational exponents, and how are they related to integer exponents?

Answers

Answer 1

Answer:

See below  

Step-by-step explanation:

Integer exponents are a subset of rational exponents

Integer exponents

An integer exponent is an exponent that is an integer. For example, in the expression y = 5³, the 3 is an integer exponent.

An integer exponent is a power. Thus, 5³ = 5× 5× 5.

Rational exponents

Rational exponents can be expressed as a ratio of integers with nonzero denominators.

Thus, in the expression [tex]y = 5^{\frac{ 2}{3 }}[/tex], the fraction ⅔ is a rational exponent.

A rational exponent is both a power and an nth root. The numerator is the power, and the denominator is the root. Thus,

[tex]5^{\frac{ 2}{ 3}} = \sqrt[3]{5^{2}} = (\sqrt[3]{5}})^{2}[/tex]


Related Questions

Write an equation to describe the relationship in this table.

Answers

Answer:

y =  x+5

Step-by-step explanation:

you cant times it by anything but 1 so x then how much does it go up by 5 so y= x+5

Answer:

1 , 5

Step-by-step explanation:

Jorge volunteers 2/3 hour at the animal shelter on wednesday. He volunteers 5 times as many hours on saturday. How many hours does Jorge volunteer on saturday?

Answers

Final answer:

To find out how many hours Jorge volunteers on Saturday, we multiply his Wednesday volunteer hours of 2/3 hour by 5, which gives us 10/3 hours or 3 1/3 hours.

Explanation:

If Jorge volunteers for 2/3 hour at the animal shelter on a Wednesday and volunteers 5 times as many hours on Saturday, we can calculate the hours he volunteers on Saturday. First, multiply the time he volunteers on Wednesday by 5:

2/3 hour × 5 = 10/3 hours, which is equivalent to 3 1/3 hours or simply 3.33 hours when converted to decimal form.

Therefore, Jorge volunteers 3 1/3 hours or 3.33 hours on Saturday at the animal shelter.

all real numbers between -4 and 6​

Answers

Final answer:

The real numbers between -4 and 6 are -3, -2, -1, 0, 1, 2, 3, 4, and 5.

Explanation:

The question asks for all real numbers between -4 and 6. In this case, the numbers between -4 and 6 are -3, -2, -1, 0, 1, 2, 3, 4, and 5.

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What is a simpler form of the expression?

(2n^2 + 5n +3)(4n - 5)

Answers

Answer:

8n³ + 10n² - 13n - 15

Step-by-step explanation:

Distribute the factors by multiplying each term in the first factor by each term in the second factor, that is

4n(2n² + 5n + 3) - 5(2n² + 5n + 3) ← distribute both parenthesis

= 8n³ + 20n² + 12n - 10n² - 25n - 15 ← collect like terms

= 8n³ + 10n² - 13n - 15

Answer:

[tex]\large\boxed{(2n^2+5n+3)(4n-5)=8n^3+10n^2-13n-15}[/tex]

Step-by-step explanation:

[tex]\text{Use FOIL:}\ (a+b)(c+d)=ac+ad+bc+bd\\\\(2n^2+5n+3)(4n-5)\\\\=(2n^2)(4n)+(2n^2)(-5)+(5n)(4n)+(5n)(-5)+(3)(4n)+(3)(-5)\\\\=8n^3-10n^2+20n^2-25n+12n-15\\\\\text{combine like terms}\\\\=8n^3+(-10n^2+20n^2)+(-25n+12n)-15\\\\=8n^3+10n^2-13n-15[/tex]

What is the standard form equation of the line shown below? (1 point) Graph of a line going through negative 2, 3 and 1, negative 3
y + 3 = −2(x − 1)
y = −2x − 1
2x + y = −1
−2x − y = 1

Answers

Answer:

y= -2x-1

Step-by-step explanation:

In solving, find the gradient from coordinates given , then use the gradient with one of the pairs to find the equation in form of y=mx+c

finding the gradient

points(-2,3) and (1,-3)

m=change in y/change in x

change in y=-3-3=-6

change in x=1--2=3

m=-6/3 =-2

taking the coordinates (1,-3) and (x,y), the equation will be

y=mx+c, where m=-2

(y--3)/(x-1) =-2

(y+3)/(x-1)= -2

(y+3) = -2(x-1)

y+3=-2x+2

y=-2x+2-3

y= -2x-1

Which best describes the graphs of the line that passes through (0,2) and (6,4) and the line that passes through (2,1) and (5,7)?

Answers

Answer:

The line which has slope 1/3 is a shallow line.

The line which has slope 2 is a steep line.

Both are increasing.

Step-by-step explanation:

Compare the lines by finding the slope between each pair of points.

Using the slope formula, substitute the points.

[tex]m = \frac{y_2-y_1}{x_2-x_1} = \frac{4-2}{6-0} = \frac{2}{6} = \frac{1}{3}[/tex]

[tex]m = \frac{y_2-y_1}{x_2-x_1} = \frac{7-1}{5-2} = \frac{6}{3} = 2[/tex]

The line which has slope 1/3 is a shallow line.

The line which has slope 2 is a steep line.

ise is shown in this scale drawing. The height of the horse in the drawing is 4.5 inches
The scale that maps the drawing to the actual horse is 1 inch to 1.5 feet.
Scale Drawing of a Horse
4.5 in
Using the scale given, enter the actual height of the horse, in feet.

Answers

6.75 feet is the actual height of the horse

What are the perpendicular sides???

Answers

Answer:

For triangle VZX, VZ and ZX are perpendicular to each other.

This is because, perpendicular sides intersect to make a right angle.

Hope this helps,

A.W.E.S.W.A.N.

Can you guys please help me out

Answers

A. ability to access cash value

hope this helps!!

15 points and show steps


Solve for x. Write the smaller solution first, and the larger solution second. -2x^2-9=-107

Answers

Answer:

x = -7 and x = 7

Step-by-step explanation:

[tex]-2x^2-9=-107\qquad\text{add 9 to both sides}\\\\-2x^2-9+9=-107+9\\\\-2x^2=-98\qquad\text{divide both sides by (-2)}\\\\\dfrac{-2x^2}{-2}=\dfrac{-98}{-2}\\\\x^2=49\to x=\pm\sqrt{49}\\\\x=-7\ \vee\ x=7[/tex]

Which statement describes what these four powers have in common?

Answers

Answer:

"All the powers have a value of 1 because the exponent is 0"

Step-by-step explanation:

To answer this, we need to recall the property that "ANYTHING to the power 0 is ALWAYS equal to 1" (except 0^0).

Here, we see that the base of all of the 4 choices are integers (and NOT ZERO) and all of them are raised to 0th power. So all of them are EQUAL TO 1.

Hence, the correct answer is "All the powers have a value of 1 because the exponent is 0"

Answer:

All the powers have a value of 1 because the exponent is 0

Step-by-step explanation:

a store manager sends an email survey to customers who have registered at the store's websites. Why is this survey biased?​

Answers

The survey is biase because it is only surveying shoppers that have registered on the website,.

Given: AD≅AO
Find: m∠OAD, m∠DBA.

Answers

[tex]OA=OD=AD=R\Rightarrow \bigtriangleup OAD\: is\: an\: equilateral\: triangle \\ \Rightarrow \widehat{AOD}=\widehat{OAD}=\widehat{ODA}=60° \\ \widehat{ABD}= \frac{\widehat{AOD}}{2} = \frac{60°}{2} = 30°[/tex]

Answer:

Step-by-step explanation:

Given: AD≅AO

To find: m∠OAD and m∠DBA.

Solution: It is given that AD≅AO, and also OA≅OD (Radius of circle), therefore ΔAOD is an equilateral triangle.

Hence, m∠OAD=m∠ODA=m∠AOD=60°.

Now, we know that the intercepted angle is half of the central angle, thus

[tex]m{\angle}DBA=\frac{m{\angle}AOD}{2}[/tex]

⇒[tex]m{\angle}DBA=\frac{60^{\circ}}{2}[/tex]

[tex]m{\angle}DBA=30^{\circ}[/tex]

Hence, the measures of [tex]{\angle}OAD[/tex] and [tex]{\angle}DBA[/tex] are [tex]60^{\circ}[/tex] and  [tex]30^{\circ}[/tex] respectively.

Use the distributive property to evaluate each expression 7(9 - 4) = ???

Answers

Answer:

7*9-7*4

63-28

35

Step-by-step explanation:

Answer:

35

Step-by-step explanation:

multiply each number in the parenthesis by the 7 outside

7(9 - 4)

= (7 × 9) + (7 × - 4) = 63 + ( - 28) = 63 - 28 = 35

A stone fell from the top of a cliff into the ocean.
In the air, it had an average speed of 16 m/s. In the water, it had an average speed of 3 m/s, before hitting the seabed. The total distance from the top of the cliff to the seabed is 127 meters, and the stone's entire fall took 12 seconds.
How long did the stone fall in the air and how long did it fall in the water?

Answers

Answer:

Time the stone fall in the air = 7 seconds

Time it fall in the water = 5 seconds

       

Step-by-step explanation:

Given in the question,

speed of stone in the air = 16 m/s

speed of stone in the water = 3m/s

The total distance from the top of the cliff to the seabed = 127 m

the total time it took to hit the seabed = 12 s

Suppose time took to hit the water = x

so the time took from top of water to seabed = 12 - x

Formula to use

distance = speed x timeTotal distance = first distance + second distance

127 = 16x +  3(12-x)

127 = 16x + 36 - 3x

127 - 36 = 16x - 3x

91 = 13x

x = 91/13

x = 7 seconds

12 - x = 12 - 7 = 5 seconds

A water dispenser has a capacity of 20,000 milliliters. What is its capacity in liters?
Be sure to include the correct unit in your answer.

Answers

Answer:

20

Step-by-step explanation:

So to get 20 all you had todo was multiply 20,000 by 0.001, because milliliters converted into liters is 1 milliliter= 0.001 liters.

Answer:

20 Liters

Step-by-step explanation:

One way to look at it is that there are 1000 mL in one L.  But I think a better way in general for  unti conversions is to do it like this.

20000 ml * [tex]\frac{1L}{1000 mL}[/tex] Where you can just cancel out the units.  Hopefully it made sense.  If you were converting from L to ml you would use [tex]\frac{1000 mL}{1 L}[/tex]

ray and hunter sell newspapers after school. ray earns $11 more than hunter. if ray earns $25,how much money does hunter earn?

Answers

Answer:

$14

Step-by-step explanation:

This should be simple, if ray earns $11 more, than hunter earns $25-$11, or $14

To find out how much Hunter earns, we subtract the $11 that Ray earns extra from Ray's total earning of $25, resulting in Hunter earning $14.

The student has asked a question regarding how much Hunter earns if Ray earns $25 which is $11 more than Hunter. To solve this, we subtract $11 from Ray's earnings to find Hunter's earnings:

Ray's earnings = $25Hunter's earnings = Ray's earnings - $11Hunter's earnings = $25 - $11Hunter's earnings = $14

Therefore, Hunter earns $14.

please help me anyone

Answers

Answer:

57 in²

Step-by-step explanation:

S=1/2*8*3=12

4s+9=4*12+9=57

In the diagram, AB CD. If m<3=115, what is m<6=?

55°

65°

75°

115°

Answers

Answer:

65°

Step-by-step explanation:

<3 + <6 = 180  because they are same side interior angles

115 + <6 = 180

Subtract 115 from each side

115-115 +<6 = 180 -115

<6 = 65

please answer quick!


A phone booth is 3 ft. by 4 ft. by 7 ft. What is the amount of space inside the phone booth?

Answers

Answer:

84

Step-by-step explanation:

3 times 4= 12

12 times 7= 84

determine if each example is positive or negative earn $25 which one is it is your feet below sea level or 4 degrees below zero​

Answers

Answer:

I would say

earned $25 is positive

0 feet below see level is negative

4 degrees below zero is negative

Step-by-step explanation:

What is the rate of change of this function?

Answers

Answer:

50 miles per day

Step-by-step explanation:

Answer:

Step-by-step explanation:

35 per day

Which vertex in EFGH corresponds with the vertex B in ABCD?

HELP PLZ!!

Answers

Answer:

F

Step-by-step explanation:

Each vertex of ABCD corresponds to the vertex of EFGH in the same position.

Parallelogram ABCD is similar to parallelogram EFGH.

Vertex A corresponds to vertex E.

Parallelogram ABCD is similar to parallelogram EFGH.

Vertex B corresponds to vertex F.

Parallelogram ABCD is similar to parallelogram EFGH.

Vertex C corresponds to vertex G.

Parallelogram ABCD is similar to parallelogram EFGH.

Vertex D corresponds to vertex H.

An estimated three out of every 25 men are left-handed what percent of the men are left-handed?

Answers

Answer:

12%

Step-by-step explanation:

3/25 x 100 = 12

Answer:12%

Step-by-step explanation:

3/25 * 100 ☺

Coterminal angle help

Answers

Answer:  320

Step-by-step explanation:

Coterminal means it is in the same place on the Unit Circle but with one or more rotations clockwise or counterclockwise.

Note: one rotation is 360°

-760 + 360 = -400

                     -400 + 360 = -40

                                           -40 + 360 = 320  

320 is between 0 and 360 so this is the angle we are looking for!

G(x)= 3/4x+6
What is the value of g(12)?

Answers

Answer:

G(12) = 15

Step-by-step explanation:

When doing g(x) equations, all you do is substitute the value inside the parentheses to x in the equation.

So you get 3/4(12) + 6.

Then simplify to get g(12) = 15

Write and Y varies directly as x. y 20 when x graph the direct variation function.

Answers

Answer:

y = 5x

Step-by-step explanation:

20 = 5(4)

20 = 20

Since they directly vary, this is a linear equation, and the slope is 5.

y = mx + b

y = 5x + b

20 = 20 + b

b = 0

So the equation is

y = 5x

If the side lengths of a cube are 14 feet, what is the correct way to write the expression to represent the volume of the cube in exponential form?

1) 14³

2) 3¹⁴

3) 14 ⋅ 3

4) 14 ⋅ 14 ⋅ 14

Answers

♫ - - - - - - - - - - - - - - - ~Hello There!~ - - - - - - - - - - - - - - - ♫

This will make sense once you see the formula:

volume = length x width x height

As it is a cube, all lengths are the same

Substitute the values in:

volume = 14 x 14 x 14

Exponents are when you multiply a value by itself

For example, 2 x 2 can be written as [tex]2^{2}[/tex]

In this case, the answer would be option 1. [tex]14^{3}[/tex]

Hope This Helps You!

Good Luck (:

Have A Great Day ^-^

↬ ʜᴀɴɴᴀʜ

Answer:

14 x 14 x 14

Step-by-step explanation:

which is an equation of the given line in standard form (-3, -1 ) (1/2, 2)​

Answers

Answer:

6x - 7y = -11

Step-by-step explanation:

To write the equation of a line when given two points, calculate the slope and substitute it into the point slope form of a line. From this form of the equation, you can simplify and convert to the standard form.

First, find the slope using the formula.

[tex]m = \frac{y_2-y_1}{x_2-x_1} =\frac{2--1}{\frac{1}{2} --3} =\frac{3}{\frac{7}{2}} = \frac{6}{7}/tex]

Substitute m = 6/7 and the point (-3,-1) into the point slope form [tex](y-y_1) = m(x-x_1)[/tex].

[tex]y--1=\frac{6}{7}(x--3)\\y + 1 = \frac{6}{7}(x+3)\\7y + 7 = 6(x + 3)\\7y + 7 = 6x + 18\\-6x + 7y + 7 = 18\\-6x + 7y = 11\\6x - 7y = -11[/tex]

To convert to standard form, multiply the equation by 7. This means each term is multiplied by 7 to clear the denominator. Then multiply using the distributive property. You will now need to move terms across the equal sign. Begin by subtracting 6x from both sides. Then subtract 7 from both side. Lastly, multiply the equation by -1 since the leading coefficient in standard form cannot be negative.

Gia went to the movies with her 7-year old daughter and her 70-year-old mother. Movie tickets are half-priced for children under 12 years old, and there is a 25% discount for senior citizens. If Gia's $8.00 ticket was the regular retail price, what percent of the full retail price did Gia pay for the three tickets?




A.60% B.66.6% C.70% D.75% ​

Answers

Answer:

D. 75%

Step-by-step explanation:

Percent of full retail price = 8+(1/2)(8)+(3/4)(8)/24

This simplifies to 0.75, which is equivalent to 75 percent.

$24 is full retail price so by dividing the amount Gia paid by it, you can find the percent of the full retail price.

Final answer:

Gia paid 75% of the full retail price for the three movie tickets.

Explanation:

To calculate the percent of the full retail price that Gia paid for the three tickets, we need to determine the total amount Gia paid and the full retail price for the three tickets.

Gia's $8.00 ticket is the regular retail price, so she paid the full price for her ticket. Her daughter's ticket is half-priced, which is $8.00 divided by 2, equaling $4.00. Her mother's ticket has a 25% discount, so she paid 75% of the full price, which is $8.00 multiplied by 0.75, equaling $6.00.

The total amount Gia paid is $8.00 + $4.00 + $6.00 = $18.00. The full retail price for the three tickets is $8.00 + $8.00 + $8.00 = $24.00. Therefore, Gia paid $18.00/$24.00 = 0.75, which is 75%, of the full retail price.

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