Suggested languages for you:

Americas

Europe

Problem 10

# Evaluate the expressions. $$\left(\frac{-2}{3}\right)^{-2}$$

Expert verified
The short answer is: $$\left(\frac{-2}{3}\right)^{-2} = \left(\frac{3}{-2}\right)^{2} = \frac{9}{4}$$.
See the step by step solution

## Step 1: Evaluate the negative exponent

Recall that a number raised to the power of a negative exponent is equal to the reciprocal of the number raised to the positive exponent: $$\left(a^{-n}\right) = \frac{1}{a^n}$$ Using this rule, we find the reciprocal of the fraction and raise it to the power of 2: $$\left(\frac{-2}{3}\right)^{-2} = \left(\frac{3}{-2}\right)^{2}$$

## Step 2: Simplify the expression

Now, raise the fraction to the power of 2 by squaring both the numerator and the denominator: $$\left(\frac{3}{-2}\right)^{2} = \frac{3^2}{(-2)^2}$$ Then compute the squares of 3 and -2: $$\frac{3^2}{(-2)^2} = \frac{9}{4}$$ The final result is $$\frac{9}{4}$$.

We value your feedback to improve our textbook solutions.

## Access millions of textbook solutions in one place

• Access over 3 million high quality textbook solutions
• Access our popular flashcard, quiz, mock-exam and notes features

## Join over 22 million students in learning with our Vaia App

The first learning app that truly has everything you need to ace your exams in one place.

• Flashcards & Quizzes
• AI Study Assistant
• Smart Note-Taking
• Mock-Exams
• Study Planner