Question

Evaluate each expression. $$125^{-2 / 3}$$

   Evaluate each expression.
$$125^{-2 / 3}$$

A Graphical Approach to Precalculus with Limits

A Graphical Approach to Precalculus with Limits

John Hornsby,… 7th Edition

Chapter 5, Problem 7

Instant Answer

Solved by Expert Nick Johnson

08/14/2020

Step 1

Recall that negative exponents mean one over that same base to that positive power. So, we can rewrite the expression as $\frac{1}{125^{2 / 3}}$. Show more…

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Evaluate each expression. $$125^{-2 / 3}$$

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Key Concepts

Properties of Exponents

This concept involves understanding the set of rules that guide how exponentiation behaves. It includes operations such as multiplying and dividing powers with the same base, raising a power to another power, working with negative exponents, and handling fractional exponents.

Negative Exponents

Negative exponents indicate the reciprocal of the base raised to the corresponding positive exponent. In other words, for any nonzero number a and exponent b, a raised to the –b is equivalent to 1 divided by a raised to the b.

Fractional Exponents

Fractional exponents combine the ideas of exponents and roots. The numerator of the fraction represents the power, and the denominator denotes the type of root. For example, raising a number to the exponent m/n means taking the nth root of the number and then raising the result to the m power, or vice versa.

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