Simplify. ((5 x^2)/(y^3))^4

Name: Problem 54, Chapter 5: Beginning and Intermediate Algebra
Uploaded: 2021-03-29T14:28:06-08:00
Duration: 1 min 27 s
Channel: Oluwaseyitan Balogun
Description: Simplify. ((5 x^2)/(y^3))^4

step 1 Hello, we're giving this expression and we're asked to simplify this. Now we're going to apply s

Question

Simplify. $$\left(\frac{5 x^{2}}{y^{3}}\right)^{4}$$

   Simplify. $$\left(\frac{5 x^{2}}{y^{3}}\right)^{4}$$

Beginning and Intermediate Algebra

Julie Miller,Molly… 3rd Edition

Chapter 5, Problem 54

Instant Answer

Solved by Expert Oluwaseyitan Balogun

03/29/2021

Step 1

This means we raise each term inside the brackets to the power of 4. This gives us: $$(5^{4} \cdot (x^{2})^{4}) \div (y^{3})^{4}$$ Show more…

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Simplify. $$\left(\frac{5 x^{2}}{y^{3}}\right)^{4}$$

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Key Concepts

Power of a Quotient Rule

This concept states that when a fraction is raised to an exponent, both the numerator and the denominator are raised to that exponent individually. It allows for the simplification of expressions in the form (a/b)^n by rewriting them as a^n divided by b^n.

Power of a Product Rule

This rule explains that when a product of factors is raised to an exponent, each factor inside the product is raised to that exponent independently. It simplifies the process of handling expressions where multiple multiplied terms are raised to a power.

Power of a Power Rule

The power of a power rule indicates that when an exponential expression is raised to another exponent, the exponents can be multiplied together. This simplifies expressions of the form (x^m)^n into x^(m*n), which is crucial when dealing with compounded exponents.

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