/*! 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 56 Simplify each exponential expres... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 0: Problem 56

Simplify each exponential expression. $$\left(10 x^{2}\right)^{-3}$$

Short Answer

Expert verified
The simplified form of the expression \((10x^2)^{-3}\) is \(1/(1000x^6)\).

Step by step solution

01

Identify the base and the exponent

The base is \(10x^2\) and the exponent is -3. This means the entire expression \((10x^2)\) is being raised to the power of -3.
02

Apply the rule of negative exponents

The rule of negative exponents states that \(a^{-n} = 1/a^n\). This means that the expression \((10x^2)^{-3}\) can be rewritten as \(1/(10x^2)^3\).
03

Simplify the expression

Now you have \(1/(10^3x^{2*3})\). To proceed, carry out the exponentiation: \(10^3=1000\) and \(2*3=6\). So, the expression simplifies to \(1/(1000x^6)\).

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

Determine whether each statement in Exercises 43鈥�50 is true or false. $$-6>2$$

Fill in each box to make the statement true. Find the exact value of \(\sqrt{13+\sqrt{2}+\frac{7}{3+\sqrt{2}}}\) without the use of a calculator.

Evaluate each algebraic expression for the given value or values of the variable(s). $$x^{2}+5 x, \text { for } x=6$$

Find the union of the sets. $$\\{1,3,5,7\\} \cup\\{2,4,6,8,10\\}$$

Factor and simplify each algebraic expression. $$(4 x-1)^{\frac{1}{2}}-\frac{1}{3}(4 x-1)^{\frac{3}{2}}$$
See all solutions

Recommended explanations on Math Textbooks

Mechanics Maths

Read Explanation

Calculus

Read Explanation

Probability and Statistics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Discrete Mathematics

Read Explanation

Logic and Functions

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.