Elementary Algebra

Published by Cengage Learning
ISBN 10: 1285194055
ISBN 13: 978-1-28519-405-9

Chapter 11 - Additional Topics - 11.3 - Fractional Exponents - Concept Quiz 11.3: 9

Answer

True.

Work Step by Step

Let us simplify the left side of the equation: $(3x^{1/6})(2x^{1/3})$ We use the associative property to remove the parentheses: $3\times x^{1/6}\times2\times x^{1/3}$ We use the commutative property to rearrange the terms: $3\times2\times x^{1/6}\times x^{1/3}$ We multiply the constants: $6x^{1/6}x^{1/3}$ To multiply powers with the same base, we add the exponents: $6x^{\frac{1}{6}+\frac{1}{3}}=6x^{1/2}$. Since this is the same as the right side of the equation, the equation is true.
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