Simplify. ((5 u^7)/(2 v^3))^4

Name: Problem 397, Chapter 6: Elementary Algebra
Uploaded: 2021-07-17T03:17:33-08:00
Duration: 1 min 1 s
Channel: Sherrie Fenner
Description: Simplify. ((5 u^7)/(2 v^3))^4

step 1 5 u to the 7 over 2b cubed all raised to the 4th so that's 5 to the 4th u to the 7 times 4 28 po

Question

Simplify. $$\left(\frac{5 u^{7}}{2 v^{3}}\right)^{4}$$

   Simplify.
$$\left(\frac{5 u^{7}}{2 v^{3}}\right)^{4}$$

Elementary Algebra

Lynn Marecek 2nd Edition

Chapter 6, Problem 397

Instant Answer

Solved by Expert Sherrie Fenner

07/17/2021

Step 1

This gives us: $$\left(\frac{5 u^{7}}{2 v^{3}}\right)^{4} = \frac{(5^{4} u^{7*4})}{(2^{4} v^{3*4})}$$ Show more…

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Simplify. $$\left(\frac{5 u^{7}}{2 v^{3}}\right)^{4}$$

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Key Concepts

Power of a Power Rule

This rule states that when a term with an exponent is raised to another exponent, the exponents are multiplied. For example, (x^m)^n equals x^(m*n). This is crucial in simplifying expressions where variables are raised to powers and then the resulting expression is raised again to a further power.

Exponentiation of a Fraction

When an entire fraction is raised to an exponent, both the numerator and the denominator are raised to that exponent individually. This rule allows one to simplify expressions of the form (a/b)^n by computing a^n and b^n separately.

Power of a Product Rule

When a product of several factors is raised to an exponent, each factor in the product is raised to that exponent separately. This means that (ab)^n equals a^n * b^n, which is used to simplify expressions where both numerical coefficients and variables are involved.

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