College Algebra 7th Edition

Published by Brooks Cole
ISBN 10: 1305115546
ISBN 13: 978-1-30511-554-5

Chapter P, Prerequisites - Section P.8 - Solving Basic Equations - P.8 Exercises: 76

Answer

$x=8$

Work Step by Step

Add 16 to both sides: $x^{\frac{4}{3}}=16$ To eliminate the rational power of $x$, raise both sides to $\frac{3}{4}$ power (the reciprocal of $\frac{4}{3}$) to obtain: $x= 16^{\frac{3}{4}}$ RECALL: $a^{\frac{m}{n}} = (\sqrt[n]{a})^m$ Use the rule above to obtain: $x= (\sqrt[4]{16})^3$ Write 16 as $2^4$ to obtain: $x=(\sqrt[4]{2^4})^3$ Simplify to obtain: $x=(2)^3 \\x=8$
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