Simplify.(x4y)3\left(\frac{x}{4y}\right)^3

x364y3\frac{$$x^3$$}{$$64y^3$$}

Simplify. ( x 4 y ) 3 \left(\frac{x}{4y}\right)^3

So let's take a look at this next practice problem here. We have our quotient x divided by four y all raised to the third power. So like other problems that we've seen before, we're gonna use our power of a quotient rule, sometimes also known as the quotient to a power property, really the same thing to solve this. So the basic idea, remember, is you're gonna take the exponent of three and you have to distribute it to everything that's inside of the parentheses in the numerator and denominator. So you distribute the x the three to the x and the exponent of three also to the denominator of four y. And then we simplify. So what we're gonna do here is we're gonna raise x to the third power. We can't really do anything with that numerator anymore. We can't simplify it. But on the bottom, we're gonna distribute this three to not only just the four, but also the y as well. So the best way to do this is to maintain the parentheses and keep it there. So we have four y raised to the third power. Because now we can see we're actually gonna have to reuse another rule to simplify this further. So sometimes you can have a power of a quotient rule that kind of will lead to a power of a product rule. In the denominator, we have this whole expression four y that's raised to the third power. That power over product rule tells us we have to distribute this three exponent to the four and also the y. So lots of problems will have you use multiple rules to simplify these expressions, and this is one of them. So on the numerator, we just don't change anything. This is still just x to the third power. We can't simplify this any further. But on the bottom, once we distribute the x one to the three to the four, you're gonna get four to the third times y to the third. You can keep that parentheses or that multiplication symbol in there or you can basically just rewrite them both with their own parentheses, either way. So what we do here is we ask ourselves, is this fully simplified? Well, with for when you take expressions like, that involve variables to exponents like x to the third and y to the third, you can't simplify those any further. But with this four to the third power, you can because four to the third power actually is a number. So, typically, when you simplify, numbers raised to exponents have to be sort of converted into the most simple forms without any exponents. And And so all we have to do for this last step is we just have to figure out what four to the third power is. So four to the third is basically just four times four times four. Four times four is sixteen, and sixteen times four is 64. So you can go ahead and work that out on the side, but this basically just equals 64. And so I'm just gonna write 64 y to the third power. Now I have all my all of my numbers raised to exponents have been simplified, and I can't do anything with the x to the third and the y to the third. So this actually is the most simplified form that I can write this expression is in, and that's the right answer. Alright? So again, multiple rules can sometimes be used in the same problem in order to simplify expressions. Thanks for watching. Hope this helped, and, we'll see you in the next one.

Simplify.(x4y)3\left(\frac{x}{4y}\$$right)^3$$

x364y3\frac{$$x^3$$}{$$64y^3$$}

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1. Review of Real Numbers2h 39m

Simplifying Fractions
30m

Evaluating Exponents
29m

Evaluating Expressions
15m

Translating Phrases to Expressions
16m

Translating Sentences to Equations
9m

The Distributive Property
17m

Simplifying Expressions
40m

2. Linear Equations and Inequalities3h 38m

The Addition and Subtraction Properties of Equality
41m

The Multiplication and Division Properties of Equality
30m

Solving Linear Equations
1h 14m

Linear Inequalities in One Variable
1h 11m

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Introduction to Problem Solving
37m

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21m

Percent Problem Solving
59m

Mixture Problem Solving
43m

4. Graphing Linear Equations in Two Variables3h 17m

The Rectangular Coordinate System
44m

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24m

Graph Linear Equations Using Intercepts
23m

Slope of a Line
44m

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38m

Point Slope Form
22m

5. Systems of Linear Equations1h 43m

Solving Systems of Linear Equations by Graphing
41m

Solving Systems of Linear Equations by Substitution
15m

Solving Systems of Linear Equations by Elimination
45m

6. Exponents and Polynomials3h 25m

The Product Rule
10m

The Quotient Rule
13m

Intro to the Power Rules
18m

The Power of a Quotient Rule
18m

Negative Exponents
28m

Simplifying Exponential Expressions Using All Exponent Rules
6m

Intro to Polynomials
21m

Adding and Subtracting Polynomials
20m

Multiplying Polynomials
33m

Special Products
34m

7. Factoring2h 42m

Factoring by Greatest Common Factor & Grouping
37m

Factoring Trinomials of the Form x² + bx + c
11m

Factoring Trinomials of the Form ax² + bx + c
37m

Factoring Special Products
33m

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41m

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Simplifying Rational Expressions
39m

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25m

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19m

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32m

Adding and Subtracting Rational Expressions with Different Denominators
32m

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44m

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28m

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23m

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15m

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5m

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24m

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27m

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19m

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23m

Introduction to Complex Numbers
18m

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51m

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25m

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1h 28m

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25m

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6. Exponents and Polynomials

The Power of a Quotient Rule

Beginning & Intermediate Algebra

6. Exponents and Polynomials

The Power of a Quotient Rule

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Multiple Choice

Simplify.
$open paren x over 4 y close paren cubed$

$the fraction with numerator x cubed and denominator 64 y$

$the fraction with numerator x cubed and denominator 4 y$

$the fraction with numerator x cubed and denominator 4 y cubed$

$the fraction with numerator x cubed and denominator 64 y cubed$

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Verified step by step guidance

Recognize that the expression is a cube of a fraction: $\left(\frac{x}{4y}\right)^3$ means you raise both the numerator and the denominator to the power of 3.

Apply the exponent to the numerator: $x^3$.

Apply the exponent to the denominator: $(4y)^3$ which means you cube both 4 and $y$ separately.

Calculate the cube of 4: \$4^3 = 64$.

Calculate the cube of $y$: $y^3$, so the denominator becomes \$64y^3$. Therefore, the simplified expression is $\frac{x^3}{64y^3}$.

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Struggling with Beginning & Intermediate Algebra?

Simplify.(x4y)3\(\left\)(\(\frac{x}{4y}\]\right\))^3

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Simplify.
$open paren x over 4 y close paren cubed$