step 1 Hello. So here we have six sevenths to the negative two. Same thing as saying one over six seven

Question

$\left(\frac{6}{7}\right)^{-2}$

Name: Problem 35, Chapter 4: Beginning and Intermediate Algebra
Uploaded: 2022-02-07T01:27:58-08:00
Duration: 22 s
Channel: Nick Johnson
Description: ((6)/(7))^-2

   $\left(\frac{6}{7}\right)^{-2}$

Beginning and Intermediate Algebra

Margaret L. Lial,… 7th Edition

Chapter 4, Problem 35

Instant Answer

Solved by Expert Nick Johnson

02/07/2022

Step 1

So, $\left(\frac{6}{7}\right)^{-2}$ is the same as $\left(\frac{7}{6}\right)^{2}$. Show more…

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$\left(\frac{6}{7}\right)^{-2}$

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Key Concepts

Exponentiation of Fractions

When dealing with fractions raised to an exponent, the exponent is applied to both the numerator and the denominator separately. This ensures that the rules of exponentiation hold true, whether the base is a whole number or a fractional value.

Properties of Exponents

This concept involves understanding the rules that govern the operations of exponents, such as the product of powers, power of a power, and division of powers. These rules are the foundation for simplifying and manipulating expressions that contain exponential terms.

Negative Exponents

Negative exponents indicate that the base should be inverted, meaning that a term raised to a negative exponent is equivalent to the reciprocal of the term raised to the corresponding positive exponent. This concept simplifies expressions by converting division into multiplication.

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