In parts (a) and (b), complete each statement. a. b^4 ·b^3=(b ·b ·b ·b)(b ·b ·b)=b^? b. b^5 ·b^5

Name: Problem 159, Chapter 0: College Algebra
Uploaded: 2022-10-05T19:27:32-08:00
Channel: Emily Himsel
Description: In parts (a) and (b), complete each statement. a. b^4 ·b^3=(b ·b ·b ·b)(b ·b ·b)=b^? b. b^5 ·b^5=(b ·b ·b ·b ·b)(b ·b ·b ·b ·b)=b^? c. Generalizing from parts (a) and (b), what should be done with the exponents when multiplying exponential expressions with the same base?

step 1 So for part A, we have B to the fourth power times B to the third power. And as indicated in que

Question

In parts (a) and (b), complete each statement. a. $b^{4} \cdot b^{3}=(b \cdot b \cdot b \cdot b)(b \cdot b \cdot b)=b^{?}$ b. $b^{5} \cdot b^{5}=(b \cdot b \cdot b \cdot b \cdot b)(b \cdot b \cdot b \cdot b \cdot b)=b^{?}$ c. Generalizing from parts (a) and (b), what should be done with the exponents when multiplying exponential expressions with the same base?

   In parts (a) and (b), complete each statement.
a. $b^{4} \cdot b^{3}=(b \cdot b \cdot b \cdot b)(b \cdot b \cdot b)=b^{?}$
b. $b^{5} \cdot b^{5}=(b \cdot b \cdot b \cdot b \cdot b)(b \cdot b \cdot b \cdot b \cdot b)=b^{?}$
c. Generalizing from parts (a) and (b), what should be done with the exponents when multiplying exponential expressions with the same base?

College Algebra

Robert Blitzer 7th Edition

Chapter 0, Problem 159

Instant Answer

Solved by Expert Emily Himsel

10/05/2022

Step 1

This can be expanded as $(b \cdot b \cdot b \cdot b)(b \cdot b \cdot b)$. Here, we are multiplying b seven times. According to the rule of exponents, when we multiply the same base, we add the exponents. So, $b^{4} \cdot b^{3}$ is equal to $b^{4+3}$. Show more…

Show all steps

Thanks for your feedback!

In parts (a) and (b), complete each statement. a. $b^{4} \cdot b^{3}=(b \cdot b \cdot b \cdot b)(b \cdot b \cdot b)=b^{?}$ b. $b^{5} \cdot b^{5}=(b \cdot b \cdot b \cdot b \cdot b)(b \cdot b \cdot b \cdot b \cdot b)=b^{?}$ c. Generalizing from parts (a) and (b), what should be done with the exponents when multiplying exponential expressions with the same base?

Play audio

Feedback

Emily Himsel and 91 other subject Algebra educators are ready to help you.

Ask a new question

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Exponentiation

Exponentiation is a mathematical operation involving a base raised to a power, where a number (the base) is multiplied by itself a specified number of times. This concept forms the basis for understanding how repetitive multiplication is represented in a compact form, which is crucial in analyzing and simplifying algebraic expressions.

Multiplication Rule for Exponents

When multiplying exponential expressions with the same base, the exponents are added together. This rule, often referred to as the product rule for exponents, holds because of the repeated multiplication definition of exponents, where combining like bases results in a summation of the counts of factors.

Please give Ace some feedback