Answer:
[tex]\displaystyle\frac{x^r}{x^s} = x^{r-s}[/tex]
Step-by-step explanation:
The quotient rule of exponential power states that:
[tex]\displaystyle\frac{x^r}{x^s} = x^{r-s}[/tex]
This can be easily understood with the help of an example:[tex]\displaystyle\frac{x^4}{x^2} = \displaystyle\frac{x\times x\times x\times x}{x\times x} = x^2 = x^{4-2}[/tex]
Basically, this quotient rule helps us to reducing the fractions. Since the numerator and the denominator is same as we have same base, we could simply subtract the powers to get the answer as illustrated in the above example.
When dividing powers with the same base, subtracting exponents simplifies the expression due to the quotient of powers rule is [tex]a^m / a^n = a^{(m - n).[/tex]
When dividing powers with the same base, subtract the exponents because of the properties of exponents.
The rule is known as the "quotient of powers" rule, and it states that when you divide two powers with the same base,
subtract the exponents to simplify the expression.
The rule can be stated as follows:
[tex]a^m / a^n = a^{(m - n).[/tex]
Here's why this rule works,
Let's say you have a number 'a' raised to two exponents 'm' and 'n':
[tex]a^m[/tex]= a × a × a ×... (m times)
[tex]a^n[/tex] = a × a × a × ... (n times)
Now, to divide these two powers, cancel out the common factors:
[tex]a^m / a^n[/tex] = (a × a × a ×... ... × a) / (a × a × a ×...... × a)
In the numerator and denominator, there are 'm' and 'n' occurrences of 'a', respectively.
Since we are dividing, we can cancel out 'n' occurrences of 'a' from the numerator and denominator:
[tex]a^m / a^n[/tex] = (a × a × a ×... ... × a) / (a × a × a ×...... × a)
= [tex]a^{(m - n)[/tex]
Therefore, when divide powers with the same base, subtract the exponents to simplify the expression and apply this property of exponents.
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plz help me on this question
8x+4(x-1) simplify the following expression
Every day a zookeeper feeds 4 adult gorillas a total of 160 lb of food. At this rate HOW many pounds of food would the zookeeper need everyday to feed 6 adult gorillas
Kelly took 12 pictures at school on Tuesday. She took 7 pictures at lunch and 5 pictures at recess. If she randomly selects a picture to put in her locker, what is the probability it is a picture she took at recess?
a 5/7
b 1/6
c 1/5
d 5/12
Anthony decided to buy two DVDs that were not included in the deal. His price after tax was $21.60. What was the cost of the two DVDs before the sales tax was added?
The cost of the two DVDs before the sales tax was added is $21.60.
To find the cost of the two DVDs before sales tax, let's first calculate the total cost including tax and then backtrack to find the cost before tax.
Calculate Total Cost with Tax:
The total cost including tax is given by: Total Cost = Price + Tax
Calculate Tax Amount:
Tax = Price * Tax Rate
Given that the sales tax rate is 8 percent (0.08 in decimal form), the tax amount is: Tax = 0.08 * $21.60 = $1.728
Calculate Total Cost:
Total Cost = Price + Tax
Total Cost = $21.60 + $1.728 = $23.328
Find Cost of DVDs Before Tax:
Let the cost of the two DVDs before tax be represented by x.
Total Cost = Price of DVDs + Price of DVDs * Tax Rate
$23.328 = x + 0.08x
$23.328 = 1.08x
Solve for x:
Divide both sides by 1.08:
x = $23.328 / 1.08 = $21.60
So, the cost of the two DVDs before the sales tax was added is $21.60.
Complete Question:
Anthony decided to buy two DVDs that we're not included in the deal. His price was $21.60. The sales tax is 8 percent. What was the cost of the two DVDs before the sales tax was added?
Rewrite as a square or a cube:
3 3/8 =_____
1 11/25=_____
Answer:
1)
3 3/8= (3/1) + (3/8)=
= (3x8)/8 + (3/8)
=(3x8 +3) / 8 putting both numbers with the same denominator
=27/8
27 is the same as 3³ 3x3x3= 27
8 is the same as 2³ 2x2x2= 8
= 3³÷ 2³
2)
1 11/25= (1/1) + (11/25)
= (25/25) + (11/25) putting both numbers with the same denominator
= (25+11)/25
=36/25
36 is the same as 6² 6x6=36
25 is the same as 5² 5x5=25
6²/5²
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Step-by-step explanation:
What does 5/9-2/3x(-1/4)=
help me please,it will be greatly appreciated
power negative a b to the third power minus AC if a equals -2 and b equals 3 and C equals negative 8
[tex]\(-ab^3 - ac = 38\)[/tex].
To evaluate the expression [tex]\(-ab^3 - ac\)[/tex] given a = -2, b = 3, and c = -8, we substitute the values into the expression:
[tex]-ab^3 - ac = -(-2)(3)^3 - (-2)(-8)\\= -(-2)(27) - (16)\\= 54 - 16 \\= 38[/tex]
ms.Jackson and 3 of her friends went out for sushi. They order 6 rolls and 4 sodas. The soda is $3.75 less than the rolls. They spent a total of $70.50. What is the cost of one roll, Write and equation and solve.
Mr Durant bought Console B for $20.99 off the advertised price. Find the total amount Mr. Durant paid.
Which statement correctly describes the relationship between the graph of f(x) and g(x)=f(x−7) ?
A. The graph of g(x) is the graph of f(x) translated 7 units left.
B. The graph of g(x) is the graph of f(x) translated 7 units up.
C. The graph of g(x) is the graph of f(x) translated 7 units right.
D. The graph of g(x) is the graph of f(x) translated 7 units down.
The statement which correctly describes the relationship between graphs related as g(x)=f(x−7) is; Choice C {The graph of g(x) is the graph of f(x) translated 7 units right}
According to the question; g(x)=f(x−7).
In essence, for every value of x on the graph (g), the value of x on the graph (f) reduces by 7.Put differently; for every value of x on the graph (f), the value of x on the graph (g) increases by 7.However, In graphs: an increase on the x axis is depicted by a movement rightward on the number line.
Therefore, if the relation g(x)=f(x−7) holds;
The graph of g(x) is the graph of f(x) translated 7 units right.
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5d - 1 = -11
What is d?
the quotient of eight and a number h is written as
grace has 2 cups of strawberries and plans to divide this amout into equal parts to make 3 strawberry pies what fracion of a cup of strawberries will be used for each pie?
What is the equation of this graphed line (-6,-3) (6,-7)
Answer: [tex]x+3y=-15[/tex]
Step-by-step explanation:
The equation of a line passes through (a,b) and (c,d) is given by :-
[tex](y-b)=\dfrac{d-b}{c-a}(x-a)[/tex]
Then, the equation of a line that passes through (-6,-3) (6,-7) will be :-
[tex](y-(-3))=\dfrac{-7-(-3)}{6-(-6)}(x-(-6))\\\\\Rightarrow y+3=\dfrac{-7+3}{6+6}(x+6)\\\\\Rightarrow\ y+3=\dfrac{-4}{12}(x+6)\\\\\Rightarrow\ y+3=\dfrac{-1}{3}(x+6)\\\\\Rightarrow\ 3(y+3)=-x-6\\\\\Rightarrow\ 3y+9=-x-6\\\\\Rightarrow\ x+3y=-15.[/tex]
Hence, the required equation is [tex]x+3y=-15[/tex].
Evaluate. (1/4)^-2 - (5^0×2)×1^-1
How can you do this problem ?? Plz explain
9n+21−3n−24 simplify
A bar of copper has a mass of 216 g and a volume of 24 cm. what is the density of copper
The density of copper bar is 9g/cm³
Given that :
Mass of copper bar = 216 g
Volume = 24 cm
Density of copper will be :
Recall :
Density = Mass / Volume
Density = 216 g / 24 cm³
Hence, Density of copper bar = 9 g/cm³
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Write these portions as percents.
A) 3 tenths and 6 hundredths.
B) 8 hundredths
C) 17 hundredths
D) 11 tenths.
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Nick and Cathy collected shells on the seashore. In the morning Nick found several shells, while Cathy found 7 shells. In the afternoon, Nick found 15 more shells. Now the ratio of Nick's shells to Cathy's shells in 3:1. How many shells did Nick find in the morning?
Thanks!!!!!!!!!!!!!!
log4 (x - 7) = 3
solve for x
It costs a family $216 to refinish a wood floor. They want to refinish floor in a larger room. The ratio of corresponding sides is 3:4. How much would it cost to refinish wood floor in the larger room?
A) $396
B) $384
C) $262
D) $288
The cost for the larger room comes out to be $384. Option B) is the correct answer.
The cost of refinishing a wood floor in a room is related to the area of the floor. Since the ratio of the corresponding sides of the two rooms is 3:4, the ratio of their areas is the square of the ratio of the sides, being 9:16 (since 32 = 9 and 42 = 16). To find the cost to refinish the larger room, we can set up a proportion where $216 corresponds to an area with a 'weight' of 9, and x corresponds to an area with a 'weight' of 16.
Mathematically this can be represented as 216/9 = x/16. Solving for x, we calculate x = (216/9) imes 16 = 24 imes 16 = $384. Therefore, the cost to refinish the wood floor in the larger room would be $384, which corresponds to option B).
It cost to refinish wood floor in the larger room is $384. So option (b) is correct.
To solve this problem, we'll use the concept of ratios to find the cost of refinishing the wood floor in the larger room.
First, let's set up the ratio of the areas of the two rooms. Since the ratio of corresponding sides is 3:4, the ratio of their areas will be 3^2 : 4^2, which is 9:16.
Now, since the cost of refinishing the smaller room is $216, we need to find what portion of the total cost that represents. Since 9 parts represent $216, 1 part represents $216 ÷ 9 = $24.
Next, we'll find the total cost of refinishing the larger room. Since the larger room has 16 parts (as per the ratio), the total cost will be 16 parts × $24/part = $384.
So, the correct answer is B) $384.
Here's the detailed calculation:
Find the ratio of areas of the rooms: [tex]\(3^2 : 4^2 = 9 : 16\)[/tex]
Find the cost per part: (216 ÷ 9 = 24)
Find the total cost for the larger room: [tex]\(16 \times 24 = 384\)[/tex]
Simplify fully: √18 / √8
which numbers represents a repeating decimal -2/5, -7, 3/9, 11/12
If 1 oz of potato chips contains 180 calories, how many ounces would contain 3,180 calories
In 17.66 ounces of chips, 3180 calories are there.
What is a unitary method?A unitary method is a mathematical way of obtaining the value of a single unit and then deriving any no. of given units by multiplying it with the single unit.
Given, 1 oz of potato chips contains 180 calories.
∴ No. of ounces of chips that contains 3180 calories can be obtained if we divide total calories by calories in 1 oz which is,
= (3180/180).
= 17.66 ounces.
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Emily has 300 books if Frank were to double the number of books that he now owns he would still have fewer than Emily has
Frank's current number of books, 'b', satisfies the inequality 2b ≤ 300, and hence, the maximum value for 'b' is 150.
1. Let's assume Frank currently owns 'b' books.
2. According to the given information, if Frank were to double the number of books he now owns, he would still have fewer books than Emily.
3. We know that Emily has 300 books. So, the inequality representing the given information is 2b ≤ 300.
4. To find the maximum value for 'b', we need to solve this inequality.
5. Dividing both sides of the inequality by 2, we get b ≤ 150.
6. This means Frank can own a maximum of 150 books in order to maintain a smaller collection than Emily's 300 books.
The detailed mathematical sentence representing this information is: Frank's current number of books, 'b', satisfies the inequality 2b ≤ 300, and hence, the maximum value for 'b' is 150.
Complete question:
Write a mathematical sentence that expresses the information given below. Use bas your variable name. If necessary: type < = to means or > = to mean . If you need to show multiplication, do not use the letter x. Use the asterisk (*) symbol instead, or simplify your answer. Emily has 300 books. If Frank were to double the number of books that he now owns, he would still have fewer than Emily has.
A gift box in the shape of a cube has a volume of 216 cm3 . What is the area of the base of the box
The area of the base of a cube with a volume of 216 cm³ is 36 cm², obtained by first calculating the side length as the cube root of the volume and then squaring that length.
The volume of a cube is calculated by raising the length of one of its sides to the third power (Volume = s³), where s is the length of a side. Given that the volume of the gift box is 216 cm³, we can find the length of a side by taking the cube root of the volume. The cube root of 216 cm³ is 6 cm, which is the length of each side of the box.
Since the base of the cube is a square, the area of the base is simply the length of a side squared (Base Area = s²). Hence, the area of the base of the box is 6 cm × 6 cm, which equals 36 cm².
Mr.hollins determines that he gives away $800 each month. If he gives away 16% of his budget, how much is his overall budget ?