Precalculus: Mathematics for Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 1305071751
ISBN 13: 978-1-30507-175-9

Chapter 1 - Section 1.2 - Exponents and Radicals - 1.2 Exercises: 4


4$^{3/2}$ = ($\sqrt[2] 4$)$^{3}$ by definition. We are here elevating 4 to the power of 3/2. We can do this in the two following ways: 4$^{3/2}$=(4$^{1/2}$)$^{3}$ = 2$^{3}$ = 8 4$^{3/2}$=(4$^{3}$)$^{1/2}$= 64$^{1/2}$= 8

Work Step by Step

Taking the square root of a number is equivalent to elevating that number to the 1/2 power. Which is why we can use Law 3 which states: (a$^{m}$)$^{n}$= (a$^{n}$)$^{m}$= a$^{mn}$. We note that the powers n and m are interchangeable.
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