/*! 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 90 Evaluate each expression without... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 0: Problem 90

Evaluate each expression without using a calculator. $$16^{-\frac{5}{2}}$$

Short Answer

Expert verified
\(\frac{1}{1024}\)

Step by step solution

01

Deal with the Negative Exponent

According to the rules of exponents, any number (except 0) with a negative exponent can be written as the reciprocal with positive exponent. Meaning, \(16^{-\frac{5}{2}}\) can be written as \( \frac{1}{16^{\frac{5}{2}}} \)
02

Break Down the Fractional Exponent

The exponent \(\frac{5}{2}\) can be dealt with in two steps: raise 16 to the 5th power, then take the square root. However, it is easier to first take the square root of 16 (since it is a perfect square) and then raise to the 5th power. This means the previous expression becomes: \( \frac{1}{(16^{\frac{1}{2}})^5} = \frac{1}{4^5} \)
03

Calculate the expression

The number raised to the power value of 5 can be computed as multiplying the number by itself five times. It denotes \(4 \times 4 \times 4 \times 4 \times 4\) which will result in 1024. So the final simplified form of the expression is: \( \frac{1}{1024} \)

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

Perform the indicated operations. $$ \left(x^{n}+2\right)\left(x^{n}-2\right)-\left(x^{n}-3\right)^{2} $$

Why is \(\left(-3 x^{2}\right)\left(2 x^{-5}\right)\) not simplified? What must be done to simplify the expression?

The mass of one hydrogen atom is \(1.67 \times 10^{-24}\) gram. Find the mass of \(80,000\) hydrogen atoms. Express the answer in scientific notation.

Evaluate each expression without using a calculator. $$27^{\frac{1}{3}}$$

In Exercises 132鈥�135, determine whether each statement makes sense or does not make sense, and explain your reasoning. There are many exponential expressions that are equal to \(36 x^{12},\) such as \(\left(6 x^{6}\right)^{2},\left(6 x^{3}\right)\left(6 x^{9}\right), 36\left(x^{3}\right)^{9},\) and \(6^{2}\left(x^{2}\right)^{6}\)
See all solutions

Recommended explanations on Math Textbooks

Pure Maths

Read Explanation

Calculus

Read Explanation

Mechanics Maths

Read Explanation

Discrete Mathematics

Read Explanation

Decision Maths

Read Explanation

Probability and 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.