Elementary Algebra

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

Chapter 11 - Additional Topics - 11.3 - Fractional Exponents - Problem Set 11.3: 26

Answer

1/4

Work Step by Step

Remember that whenever a number in the numerator of a fraction is raised to a negative power, we put the number in the denominator of the fraction and make the exponent positive. Thus, we find: $8^{-2/3} = 1/(8^{2/3})$ Now, recall the formula:$ a^{b/c}=( \sqrt[c] {a})^{b}$. Thus, we obtain: $1/(8^{2/3})=1/(\sqrt[3] {8})^{2}=1/(2^{2})=1/4$
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