Chapter 0: Chapter 0

Problem 10

Next question

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

Short Answer

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 by step solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

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 $\frac{9}{4}$.

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Recommended explanations on Math Textbooks

Find Study Materials for

Create Study Materials

Select your language

Chapter 0: Chapter 0

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

Short Answer

Step by step solution

Unlock all solutions

Step 1: Evaluate the negative exponent

Step 2: Simplify the expression

Access millions of textbook solutions in one place

Most popular questions from this chapter

More chapters from the book ‘Finite Mathematics and Applied Calculus’

Chapter 1

Chapter 2

Chapter 3

Chapter 4

Chapter 5

Chapter 6

Chapter 7

Chapter 8

Chapter 9

Chapter 10

Chapter 11

Chapter 12

Chapter 13

Chapter 14

Chapter 15

Chapter 16

Join over 22 million students in learning with our Vaia App

Recommended explanations on Math Textbooks

Mechanics Maths

Probability and Statistics

Decision Maths

Statistics

Geometry

Pure Maths