step 1 The given expression is 5 multiplied by x x x to the power 2 multiplied by 4 raised to the power

Question

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

Name: Problem 45, Chapter 5: Beginning and Intermediate Algebra
Uploaded: 2021-03-21T15:21:14-08:00
Duration: 1 min 8 s
Channel: Prashansha Kaushik
Description: Simplify. 5(x^2 y)^4

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

Beginning and Intermediate Algebra

Julie Miller,Molly… 3rd Edition

Chapter 5, Problem 45

Instant Answer

Solved by Expert Prashansha Kaushik

03/21/2021

Step 1

So, we can rewrite the expression as follows: $$5\left(x^{2} y\right)^{4} = 5x^{2*4}y^{4}$$ Show more…

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

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Key Concepts

Exponentiation of a Product

This concept states that when a product of factors is raised to a power, the exponent is distributed to each factor in the product. In algebraic expressions, this is represented by (ab)^n = a^n * b^n, which allows for the simplification of products raised to an exponent.

Power of a Power Rule

This rule describes how to handle situations when an exponential expression is raised to another power. It states that (a^m)^n equals a^(m*n), ensuring that multiple layers of exponents are combined correctly during the simplification process.

Algebraic Simplification

This is the process of rewriting expressions in a simpler or more standard form by applying algebraic rules such as exponent rules, distribution, and combining like terms. This concept is essential to reduce complex expressions to a form that is easier to interpret and work with.

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