Algebra 1: Common Core (15th Edition)

Published by Prentice Hall
ISBN 10: 0133281140
ISBN 13: 978-0-13328-114-9

Chapter 7 - Exponents and Exponential Functions - 7-5 Rational Exponents and Radicals - Practice and Problem-Solving Exercises - Page 451: 41

Answer

$42x$.

Work Step by Step

The given expression is $=(36x)^{\frac{1}{2}}(49x)^{\frac{1}{2}}$ Rewrite as square terms. $=(6^2x)^{\frac{1}{2}}(7^2x)^{\frac{1}{2}}$ Raise each factor to the second power. $=6^{(2\cdot \frac{1}{2})}x^{\frac{1}{2}}7^{(2\cdot \frac{1}{2})}x^{\frac{1}{2}}$ Simplify. $=6x^{\frac{1}{2}}7x^{\frac{1}{2}}$ Add exponents of powers with the same base. $=6\cdot 7x^{\frac{1}{2}+\frac{1}{2}}$ Simplify. $=42x^{\frac{1+1}{2}}$ $=42x^{\frac{2}{2}}$ $=42x$.
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