/*! 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 48 $$ 16^{-\frac{1}{2}} $$ A.... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 3: Problem 48

$$ 16^{-\frac{1}{2}} $$ A. 8 B. \(\frac{1}{4}\) C. \(-\frac{1}{4}\) D. -4

Short Answer

Expert verified
The value of \( 16^{-\frac{1}{2}} \) is \( \frac{1}{4} \), so the correct answer is B.

Step by step solution

01

Understand the given expression

The given expression is \( 16^{-\frac{1}{2}} \). Here, 16 is the base and \( -\frac{1}{2} \) is the exponent.
02

Rewrite the expression

The negative exponent indicates that we need to take the reciprocal of the base raised to the positive exponent. So, \( 16^{-\frac{1}{2}} \) can be rewritten as \( \frac{1}{16^{\frac{1}{2}}} \).
03

Calculate the positive exponent

Next, compute \( 16^{\frac{1}{2}} \). This represents the square root of 16. The square root of 16 is 4. Therefore, \( 16^{\frac{1}{2}} = 4 \).
04

Simplify the reciprocal

Now, substitute 4 back into the expression \( \frac{1}{16^{\frac{1}{2}}} \). This becomes \( \frac{1}{4} \).
05

Final Answer

The value of \( 16^{-\frac{1}{2}} \) is \( \frac{1}{4} \). Therefore, the correct answer is B.

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!

Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Negative Exponents
In mathematics, dealing with negative exponents might seem tricky initially. But, they are simpler than they appear. When you encounter a negative exponent, it indicates that you need to take the reciprocal of the number raised to the corresponding positive exponent.
Let's break it down:
  • For instance, if you have a number like \( a^{-n} \), it becomes \( \frac{1}{a^n} \). This is the basic principle of negative exponents.
  • To put it another way, the negative sign in the exponent tells you to 'flip' the number into its reciprocal.
Applying this concept to our exercise, the negative exponent \( 16^{-\frac{1}{2}} \) becomes \( \frac{1}{16^{\frac{1}{2}}} \). This simple flipping transforms the problem into one that's easier to solve!
Reciprocals
Reciprocals are a fundamental concept in mathematics that you鈥檒l come across quite often. The reciprocal of a number is 1 divided by that number.
  • For example, the reciprocal of 5 is \( \frac{1}{5} \).
  • If you have a fraction, the reciprocal is simply flipping the numerator and the denominator. So, the reciprocal of \( \frac{2}{3} \) is \( \frac{3}{2} \).
  • It鈥檚 also important to understand that the product of a number and its reciprocal is always 1. For instance, \( a \times \frac{1}{a} = 1 \).
In our exercise, we use this concept when we change \( 16^{-\frac{1}{2}} \) to \( \frac{1}{16^{\frac{1}{2}}} \). By flipping 16 to \( \frac{1}{16} \), we simplify the problem immensely!
Square Roots
Square roots are quite common in mathematics and help simplify various problems, especially when dealing with exponents.
The square root of a number is a value that, when multiplied by itself, gives the original number.
  • For example, the square root of 9 is 3, because \( 3 \times 3 = 9 \).
  • It is represented as \( \sqrt{9} \) or \( 9^{1/2} \). They mean the same thing!
In our exercise, after handling the negative exponent, we need to find \( 16^{\frac{1}{2}} \). This means finding the square root of 16.
Since \( 4 \times 4 = 16 \), the square root of 16 is 4. Plugging this back into our formula converts \( \frac{1}{16^{\frac{1}{2}}} \) into \( \frac{1}{4} \). This solves our initial problem, giving us the final answer.

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

Eli's daughter had a birthday party at Molly Mouse's Pizza Planet. There were two tables of girls. The girls left to play the games and Eli saw that one table had left \(\frac{1}{2}\) of a pie and the other had left \(\frac{2}{3}\) of a pie. Eli added the two and came up with one full pie and one piece left over. What is the smallest number of pieces that each pie was cut into? Write your answer in the box.

\(\frac{11}{45}\) multiplied by its reciprocal equals Write your answer in the blank.

$$ \frac{1}{7}+\frac{3}{5}+\frac{2}{10}= $$ Write the correct numerator and denominator in the boxes.

$$ \begin{aligned} &\frac{3}{54}-\frac{3}{56}\\\ &\begin{array}{|l|l|} \hline \text { Select... } & \nabla \\ \hline> \\ \hline< \\ \hline= \\ \hline \end{array} \end{aligned} $$

A company claims its soap is \(99 \frac{44}{100}\) percent pure. What is \(\frac{44}{100}\) reduced to its lowest form? A. \(\frac{44}{100}\) B. \(\frac{22}{50}\) C. \(\frac{11}{25}\) D. \(\frac{4}{10}\)
See all solutions

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Read Explanation

Pure Maths

Read Explanation

Decision Maths

Read Explanation

Calculus

Read Explanation

Logic and Functions

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.