Simplify. (-m^7 n^3)^5

Name: Problem 63, Chapter 5: Beginning and Intermediate Algebra
Uploaded: 2021-04-01T15:02:04-08:00
Duration: 45 s
Channel: Erika Bustos
Description: Simplify. (-m^7 n^3)^5

step 1 We need to simplify the following expression. So this expression is really negative 1 times m to

Question

Simplify. $$\left(-m^{7} n^{3}\right)^{5}$$

   Simplify. $$\left(-m^{7} n^{3}\right)^{5}$$

Beginning and Intermediate Algebra

Julie Miller,Molly… 3rd Edition

Chapter 5, Problem 63

Instant Answer

Solved by Expert Erika Bustos

04/01/2021

Step 1

This gives us $(-1)^{5} \cdot m^{7 \cdot 5} \cdot n^{3 \cdot 5}$. Show more…

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Simplify. $$\left(-m^{7} n^{3}\right)^{5}$$

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Key Concepts

Power of a Product Rule

This rule states that when a product of factors is raised to a power, each factor is raised to that power individually. Mathematically, (ab)^n = a^n * b^n, which simplifies the process of handling complex expressions with multiple variables or terms.

Power of a Power Rule

This rule explains that when an exponential expression is raised to another power, the exponents multiply. In formula terms, (a^m)^n = a^(m*n), thereby facilitating the simplification of expressions where a power is taken of another power.

Handling Negative Base Exponentiation

When raising a negative base to a power, it is important to consider the parity of the exponent. If the exponent is an even number, the negative sign is neutralized resulting in a positive outcome, while if it is odd, the negative sign persists in the final result.

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