Problem

Use the Law of Exponents to rewrite and simplify …

01:41

Question

Answered step-by-step

Problem 2 Easy Difficulty

Use the Law of Exponents to rewrite and simplify the expression.

(a) $ 8^\frac{4}{3} $
(b) $ x (3x^2)^3 $

Video Answer

Solved by verified expert

Textbook Answer

Official textbook answer

Video by Heather Zimmers

Numerade Educator

This textbook answer is only visible when subscribed! Please subscribe to view the answer

Missouri State University

Watch More Solved Questions in Chapter 1

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

Problem 6

Problem 7

Problem 8

Problem 9

Problem 10

Problem 11

Problem 12

Problem 13

Problem 14

Problem 15

Problem 16

Problem 17

Problem 18

Problem 19

Problem 20

Problem 21

Problem 22

Problem 23

Problem 24

Problem 25

Problem 26

Problem 27

Problem 28

Problem 29

Problem 30

Problem 31

Problem 32

Problem 33

Problem 34

Problem 35

Problem 36

Problem 37

Problem 38

Video Transcript

Okay, so we want to use exponents rules to simplify these expressions. And so, first of all, if you think about the number eight, think of it as a power of two. So eight is the same as two cubed. So we have two cubed to the 4/3 power. Now, remember, your exponents rule the power rule that says if you have a power to a power, you're going to multiply them. So we're going to multiply three times 4/3 and three times 4/3 is for So now all we have is to to the fourth and that 16 for part B. We're going to raise three x squared to the third power by raising each of those factors to the third power. So we have our X, and then we have three to the third power, and then we have X squared to the third power. And just like we saw in part A, we're going to use the power rule and multiply the powers two and three. So now we have X times three cubed, which is 27 times X to the sixth power. Now, remember that that X in the front is really X to the first power and you can add the exponents on X and you will get X to the seventh. So we have 27 times X to the seventh power.

Get More Help with this Textbook

James Stewart

Calculus: Early Transcendentals

View More Answers From This Book

Find Another Textbook

Study Groups

Study with other students and unlock Numerade solutions for free.

Problem