step 1 Hello, so here we have 7 to the 4th cubed. So this is we have a power to a power, we multiply ou

Question

$\frac{\left(7^{4}\right)^{3}}{7^{9}}$

Name: Problem 77, Chapter 4: Beginning and Intermediate Algebra
Uploaded: 2022-02-07T03:14:07-08:00
Duration: 27 s
Channel: Nick Johnson
Description: ((7^4)^3)/(7^9)

   $\frac{\left(7^{4}\right)^{3}}{7^{9}}$

Beginning and Intermediate Algebra

Margaret L. Lial,… 7th Edition

Chapter 4, Problem 77

Instant Answer

Solved by Expert Nick Johnson

02/07/2022

Step 1

Here, $a = 7$, $m = 4$, and $n = 3$. So, we have: \[(7^{4})^{3} = 7^{4 \times 3} = 7^{12}\] Show more…

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$\frac{\left(7^{4}\right)^{3}}{7^{9}}$

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Key Concepts

Quotient Rule for Exponents

The Quotient Rule for Exponents states that when dividing two exponential expressions with the same base, you subtract the exponent in the denominator from the exponent in the numerator. This rule is represented as a^(m)/a^(n) = a^(m-n) and is essential for simplifying divisions involving exponents.

Exponentiation

Exponentiation is a mathematical operation that involves raising a base number to a power, representing repeated multiplication of the base. It is a fundamental concept in algebra that simplifies expressions and calculations involving repeated multiplications.

Power of a Power Rule

The Power of a Power Rule states that when an exponential expression is raised to another power, the exponents are multiplied together. This rule is expressed as (a^m)^n = a^(m*n), and it is crucial for simplifying nested exponential expressions.

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