Simplify. ( y 4 5 ) 3 \left(\frac{y^4}{5}\right)^3

So, let's take a look at our next practice problem. We have a quotient y to the fourth power over five all raised to the third power. Whenever we see quotients raised to exponents, we use the power of the quotient rule. If you remember the way this works, we're going to use the exponent of three distributed to everything that's inside the numerator and also everything that is inside the denominator and then we're going to simplify. So, on the top what we get is you're going to get y to the fourth power raised to the third power. Now, if you write it like this, it's very easy to get those powers confused. So, typically whenever you have things like this, you're gonna keep the parentheses in the numerator, and then on the bottom, it's a little bit more straightforward because all we just have is a single number raised to a power, so we don't need that parentheses there, but you could write it if you really need to. Alright? Now, on the top, we can simplify this further because we have a power that is raised to another power. We've seen this rule before. The basic idea is that when you have a power to a power, then you can so we can, multiply those exponents together. This is really like you have y to the fourth power times itself three times, and so you can multiply those exponents. On the bottom, we just have y five raised to the third power, and that's a number. Five raised to the third power is just five times five times five. So, if you simplify this, this is really just five times five times five. This is 25 times five, and this ends up being 125. Alright? So, on the bottom here, we just get 125. On the top, what ends up happening here is we get four times three for the exponent, so this just becomes 12. Why did the 12 over 125? Can we simplify this last expression any further? No, because we just have variables raised to exponents, can't simplify that. And a 125, there's nothing here we can cancel. There's no like terms or anything like that, so we can go ahead and just say that this is our most simplified answer. Alright. That's really all there is to it for, this one. Let me know if you have any questions, and I'll see you in the next

Table of contents

Skip topic navigation

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

3. Solving Word Problems2h 43m

Introduction to Problem Solving
37m

Formulas
21m

Percent Problem Solving
59m

Mixture Problem Solving
43m

4. Graphing Linear Equations in Two Variables3h 17m

The Rectangular Coordinate System
44m

Graph Linear Equations in Two Variables
24m

Graph Linear Equations Using Intercepts
23m

Slope of a Line
44m

Slope-Intercept Form
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

Quadratic Equations & Applications
41m

8. Rational Expressions and Equations3h 13m

Simplifying Rational Expressions
39m

Multiplying and Dividing Rational Expressions
25m

Adding and Subtracting Rational Expressions with Common Denominators
19m

Least Common Denominators
32m

Adding and Subtracting Rational Expressions with Different Denominators
32m

Rational Equations
44m

9. Inequalities and Absolute Value2h 52m

Set Operations and Compound Inequalities
42m

Absolute Value Equations
38m

Absolute Value Inequalities
39m

Linear Inequalities in Two Variables
28m

Systems of Linear Inequalities
23m

10. Relations and Functions2h 9m

Introduction to Relations and Functions
57m

Function Notation
15m

Graphing Common Functions
5m

Composition of Functions
24m

Direct & Inverse Variation
27m

11. Roots, Radicals, and Complex Numbers2h 45m

Introduction to Radical Expressions
24m

Simplifying Radical Expressions
27m

Adding and Subtracting Radicals
19m

Multiplying, Dividing, and Rationalizing Radicals
23m

Introduction to Complex Numbers
18m

Multiplying and Dividing Complex Numbers
51m

12. Quadratic Equations and Functions3h 1m

The Square Root Property
25m

Completing the Square
26m

The Quadratic Formula
40m

Graphing Quadratic Equations
1h 28m

13. Inverse, Exponential, & Logarithmic Functions1h 5m

Introduction to Inverse Functions
25m

Exponential Functions
13m

Introduction to Logarithmic Functions
26m

14. Conic Sections & Systems of Nonlinear Equations58m

Graphing Circles
32m

Ellipses
15m

Parabolas
10m

15. Sequences, Series, and the Binomial Theorem1h 46m

Introduction to Sequences
40m

Arithmetic Sequences
27m

Geometric Sequences
26m

Factorials
11m

6. Exponents and Polynomials

The Power of a Quotient Rule

Beginning & Intermediate Algebra

6. Exponents and Polynomials

The Power of a Quotient Rule

Previous problemNext problem

Struggling with Beginning & Intermediate Algebra?

Join thousands of students who trust us to help them ace their exams!

Multiple Choice

Simplify.
${(\frac{y^{4}}{5})}^{3}$

$\frac{y^{64}}{125}$

$\frac{y^{12}}{125}$

$\frac{y^{12}}{5}$

$\frac{y^{4}}{125}$

0 Comments

Previous problemNext problem

Verified step by step guidance

Identify the expression to simplify: $\left(\frac{y^4}{5}\right)^3$.

Apply the exponent to both the numerator and the denominator inside the parentheses separately, using the rule $\left(\frac{a}{b}\right)^n = \frac{a^n}{b^n}$, so rewrite as $\frac{\left(y^4\right)^3}{5^3}$.

Use the power of a power rule for exponents on the numerator: $\left(y^4\right)^3 = y^{4 \times 3} = y^{12}$.

Calculate the denominator by raising 5 to the power of 3: \$5^3 = 125$.

Write the simplified expression as $\frac{y^{12}}{125}$.

5:14m

Watch next

Master Power of a Quotient Rule with a bite sized video explanation from Patrick Ford

Struggling with Beginning & Intermediate Algebra?

Simplify.(y45)3\(\left\)(\(\frac{y^4}{5}\]\right\))^3

Watch next

Simplify.
${(\frac{y^{4}}{5})}^{3}$