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 24m

Simplifying Fractions
30m

Evaluating Exponents
14m

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 42m

The Addition and Subtraction Properties of Equality
47m

The Multiplication and Division Properties of Equality
30m

Solving Linear Equations
1h 14m

Solving Linear Inequalities
1h 8m

3. Solving Word Problems2h 48m

Introduction to Problem Solving
37m

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21m

Percent Problem Solving
1h 4m

Mixture Problem Solving
43m

4. Graphing4h 42m

The Rectangular Coordinate System
44m

Graph Linear Equations in Two Variables
24m

Graph Linear Equations Using Intercepts
23m

Slope of a Line
44m

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38m

Point Slope Form
22m

Linear Inequalities in Two Variables
28m

Introduction to Relations and Functions
40m

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15m

5. Systems of Linear Equations2h 6m

Solving Systems of Linear Equations by Graphing
41m

Solving Systems of Linear Equations by Substitution
15m

Solving Systems of Linear Equations by Elimination
45m

Systems of Linear Inequalities
23m

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

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33m

Special Products
34m

7. Factoring2h 36m

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

Quadratic Equations & Applications
35m

8. Rational Expressions and Equations3h 51m

Simplifying Rational Expressions
39m

Multiplying and Dividing Rational Expressions
25m

Adding and Subtracting Rational Expressions with Common Denominators
24m

Least Common Denominators
32m

Adding and Subtracting Rational Expressions with Different Denominators
39m

Rational Equations
44m

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27m

9. Roots and Radicals1h 21m

Introduction to Radical Expressions
11m

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26m

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19m

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23m

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17m

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24m

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29m

Introduction to Complex Numbers
18m

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51m

Complex Solutions of Quadratic Equations
10m

Graphing Quadratic Equations
30m

6. Exponents and Polynomials

The Power of a Quotient Rule

Beginning 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 power 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 raise both 4 and y to the power of 3 separately.

Calculate \$4^3$ which is $64$, and $y^3$ remains as $y^3$.

Combine the results to write the simplified expression as $\frac{x^3}{64y^3}$.

5:14m

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Struggling with Beginning Algebra?

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

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