/*! 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 11 Write each expression using a si... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 11

Write each expression using a single exponent. Check your answers with a calculator. a. \(5^{3} \cdot 5^{8}\) b. \(9^{2} \cdot 9^{5}\) c. \(7^{4} \cdot 7^{7}\) d. \(7^{5} \cdot 7^{0}\)

Short Answer

Expert verified
Question: Simplify the following expressions and check your answer using a calculator: a. \(5^{3} \cdot 5^{8}\) b. \(9^{2} \cdot 9^{5}\) c. \(7^{4} \cdot 7^{7}\) d. \(7^{5} \cdot 7^{0}\) Answer: a. \(5^{11}= 48828125\) b. \(9^{7}= 4782969\) c. \(7^{11}= 1977326743\) d. \(7^{5}= 16807\)

Step by step solution

01

Apply the exponent rule

To solve each expression, we will apply the exponent rule: \(a^{m} \cdot a^{n} = a^{m+n}\). This rule states that when multiplying two exponential expressions with the same base, the exponents can be added. Apply this rule to each expression: a. \(5^{3} \cdot 5^{8}\) b. \(9^{2} \cdot 9^{5}\) c. \(7^{4} \cdot 7^{7}\) d. \(7^{5} \cdot 7^{0}\)
02

Simplify the expressions

Next, simplify each expression by adding the exponents. a. \(5^{3+8} = 5^{11}\) b. \(9^{2+5} = 9^{7}\) c. \(7^{4+7} = 7^{11}\) d. \(7^{5+0} = 7^{5}\) Now let's check the answers using a calculator.
03

Check the answers with a calculator

Check each simplified expression: a. \(5^{11} = 48828125\) b. \(9^{7} = 4782969\) c. \(7^{11} = 1977326743\) d. \(7^{5} = 16807\) By following the rule for combining exponents and using a calculator to check the results, we have confirmed that the given expressions have been correctly simplified.

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 of the following numbers is even or odd. In each case, give a reason for your answer. a. 22,225 b. 13,578 c. 1500
Calculate the following. As part of your answer, identify the quotient and remainder (if any). a. \(56 \div 7\) b. \(112 \div 4\) c. \(95 \div 3\) d. \(222 \div 11\) e. \(506 \div 13\) f. \(587 \div 23\) g. \(0 \div 15\) h. \(15 \div 0\)
a. Subtract the year in which you were born from this year. b. Is the difference you obtain your age? c. Have you had your birthday yet this year? Does this affect your answer in part b?
Explain why 90,210 is less than 91,021.
a. List all possible factorizations of 30 and 105 . b. How many different factorizations do each of these numbers have?
See all solutions

Recommended explanations on Math Textbooks

Statistics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Calculus

Read Explanation

Probability and Statistics

Read Explanation

Applied Mathematics

Read Explanation

Geometry

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.