Simplify. ((3 m^5)/(5 n))^3

Name: Problem 395, Chapter 6: Elementary Algebra
Uploaded: 2021-07-17T03:13:07-08:00
Duration: 51 s
Channel: Sherrie Fenner
Description: Simplify. ((3 m^5)/(5 n))^3

step 1 3M to the 5 over 5n, all raise to the third power. So I have 3 to the 3rd, M to the 5 times 3, w

Question

Simplify. $$\left(\frac{3 m^{5}}{5 n}\right)^{3}$$

   Simplify.
$$\left(\frac{3 m^{5}}{5 n}\right)^{3}$$

Elementary Algebra

Lynn Marecek 2nd Edition

Chapter 6, Problem 395

Instant Answer

Solved by Expert Sherrie Fenner

07/17/2021

Step 1

This gives us: $$\left(\frac{3 m^{5}}{5 n}\right)^{3} = \frac{3^{3} (m^{5})^{3}}{(5 n)^{3}}$$ Show more…

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Simplify. $$\left(\frac{3 m^{5}}{5 n}\right)^{3}$$

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Key Concepts

Simplification of Algebraic Expressions

This concept involves applying the rules of exponents and the power of a quotient rule to reduce complex expressions to simpler forms. It includes careful handling of numeric and variable components to achieve a clear and concise simplified expression.

Power of a Quotient Rule

This rule states that when a fraction is raised to an exponent, both the numerator and the denominator are raised to that exponent independently. It ensures that the operation is applied uniformly to each part of the fraction.

Properties of Exponents

These properties include rules like the power of a product and the power of a power. They allow us to simplify expressions by multiplying the exponents in expressions where a power is raised to another power or by distributing an exponent across factors in a product.

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