/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 9 Evaluate the expressions. $$ ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 0: Problem 9

Evaluate the expressions. $$ \left(\frac{1}{4}\right)^{-2} $$

Short Answer

Expert verified
The short answer to the question is to apply the rules of exponents and fractions to evaluate the expression as follows: \(\left(\frac{1}{4}\right)^{-2} = \left(\frac{4}{1}\right)^{2} = \frac{4^2}{1^2} = \frac{16}{1} = 16\). Therefore, the value of \(\left(\frac{1}{4}\right)^{-2}\) is 16.

Step by step solution

01

Make the exponent positive

Since we have a negative exponent, the first thing we need to do is make it positive. To do this, we can use the rule \((a^{-n}) = \frac{1}{a^n}\), which means that we can rewrite the expression by inverting the base (the fraction) and changing the exponent to positive. So, we have: \[ \left(\frac{1}{4}\right)^{-2} = \left(\frac{4}{1}\right)^{2} \]
02

Raise the fraction to the power

The next step is to raise the fraction \(\frac{4}{1}\) to the power of 2. To do this, we apply the exponent to both the numerator and the denominator. Here's the formula: \(a^n = a^n\) \[ \left(\frac{4}{1}\right)^{2} = \frac{4^2}{1^2} \]
03

Simplify the expression

Now, we need to simplify the expression by evaluating the powers in the numerator and the denominator. \[ \frac{4^2}{1^2} = \frac{16}{1} \] Since any number divided by 1 is equal to itself, the final expression is: \[ \frac{16}{1} = 16 \] So, the value of \(\left(\frac{1}{4}\right)^{-2}\) is 16.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

\(\left(y^{3}+2 y^{2}+y\right)\left(y^{2}+2 y-1\right)\)

Solve the equation for \(x\) (mentally, if possible). \(a x+b=c \quad(a \neq 0)\)

\(y^{2}-4 y\)

\(10 x\left(x^{2}+1\right)^{4}\left(x^{3}+1\right)^{5}+15 x^{2}\left(x^{2}+1\right)^{5}\left(x^{3}+1\right)^{4}\)

Convert each expression in Exercises into its technology formula equivalent as in the table in the text.\(3+\frac{3+x}{x y}\)
See all solutions

Recommended explanations on Math Textbooks

Pure Maths

Read Explanation

Probability and Statistics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Calculus

Read Explanation

Discrete Mathematics

Read Explanation

Statistics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.