/*! 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 34 Rewrite with a positive exponent... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 10: Problem 34

Rewrite with a positive exponent and evaluate. \(100^{-1 / 2}\)

Short Answer

Expert verified
The expression \(100^{-\frac{1}{2}}\) rewritten with a positive exponent and evaluated is \(\frac{1}{10}\).

Step by step solution

01

Rewrite expression with a positive exponent

To rewrite \(100^{-\frac{1}{2}}\) with a positive exponent, we need to find the reciprocal of the base 100 and change the negative power to a positive one. So, \(100^{-\frac{1}{2}} = (\frac{1}{100})^{\frac{1}{2}}\)
02

Evaluate the expression

Now that we have the expression \((\frac{1}{100})^{\frac{1}{2}}\), we can evaluate it by finding the square root of \(\frac{1}{100}\). \((\frac{1}{100})^{\frac{1}{2}} = \sqrt{\frac{1}{100}}\) Since the square root of a fraction can be expressed as the square root of its numerator divided by the square root of its denominator, we have: \(\sqrt{\frac{1}{100}} = \frac{\sqrt{1}}{\sqrt{100}} = \frac{1}{10}\) The expression \(100^{-\frac{1}{2}}\) rewritten with a positive exponent and evaluated is \(\frac{1}{10}\).

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
Negative exponents might look intimidating at first, but they are actually quite simple to understand. An exponent indicates how many times a number, known as the base, is multiplied by itself. When the exponent is negative, it indicates the reciprocal of the base raised to the corresponding positive power.
For example:
  • If you have a negative exponent like \(a^{-n}\), it can be rewritten as \(\frac{1}{a^n}\).
  • This operation shifts the base \(a\) from the numerator to the denominator or vice versa, thus creating the reciprocal.
A practical example: In the expression \(100^{-\frac{1}{2}}\), the negative exponent transforms this into the reciprocal of \(100^{\frac{1}{2}}\). Therefore, when a number bears a negative exponent, you're essentially finding the reciprocal of exponentiating it with a positive number. This understanding helps us manipulate and simplify expressions in algebra easily.
Reciprocal
To understand negative exponents, you need to grasp the concept of a reciprocal. A reciprocal is simply one divided by the number. It's like flipping a number over.
  • The reciprocal of \(x\) is \(\frac{1}{x}\).
  • Conversely, the reciprocal of \(\frac{1}{x}\) is \(x\).
Knowing this helps a great deal in mathematics. For instance, when dealing with the expression \(100^{-\frac{1}{2}}\), rewriting it involves finding the reciprocal of 100 raised to the power of \(\frac{1}{2}\). This becomes \((\frac{1}{100})^{\frac{1}{2}}\).
Understanding reciprocals is crucial, especially when you're simplifying algebraic expressions or solving equations that involve fractions and exponents.
Square Roots
Square roots are a fundamental concept of numbers. They are the opposite of squaring a number.
  • For any given number \(a\), its square root, denoted as \(\sqrt{a}\), is a value that when multiplied by itself gives \(a\).
  • For example, the square root of 100 is 10 because \(10 \times 10 = 100\).
Square roots come into play when evaluating expressions like the one we solved, \((\frac{1}{100})^{\frac{1}{2}}\). Here, we find the square root of \(\frac{1}{100}\), which equals \(\frac{1}{10}\), as \(\sqrt{1} = 1\) and \(\sqrt{100} = 10\).
Being comfortable with finding square roots allows you to solve various mathematical problems, especially in terms of simplifying expressions with fractional exponents.

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

Find the conjugate of each binomial. Then, multiply the binomial by its conjugate. $$(\sqrt{p}+5)$$

Rationalize the denominator of each expression. Assume all variables represent positive real numbers. $$\frac{6}{\sqrt[3]{4}}$$

Simplify completely. $$\frac{5+10 \sqrt{3}}{5}$$

Rationalize the denominator of each expression. $$\frac{1}{\sqrt{6}}$$

Rationalize the denominator of each expression. Assume all variables represent positive real numbers. $$\sqrt[4]{\frac{2}{9}}$$
See all solutions

Recommended explanations on Math Textbooks

Logic and Functions

Read Explanation

Decision Maths

Read Explanation

Calculus

Read Explanation

Discrete Mathematics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Applied Mathematics

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.