Intermediate Algebra for College Students (7th Edition)

Published by Pearson
ISBN 10: 0-13417-894-7
ISBN 13: 978-0-13417-894-3

Chapter 7 - Section 7.2 - Rational Exponents - Exercise Set - Page 522: 75



Work Step by Step

RECALL: (1) $a^m \cdot a^n = a^{m+n}$ (2) $\dfrac{a^m}{a^n} = a^{m-n}$ Use rule (1) above to obtain: $=\dfrac{3^{\frac{1}{2}+\frac{3}{4}}}{3^{\frac{1}{4}}} \\=\dfrac{3^{\frac{2}{4}+\frac{3}{4}}}{3^{\frac{1}{4}}} \\=\dfrac{3^{\frac{2+3}{4}}}{3^{\frac{1}{4}}} \\=\dfrac{3^{\frac{5}{4}}}{3^{\frac{1}{4}}}$ Use rule (2) above to obtain: $=3^{\frac{5}{4} - \frac{1}{4}} \\=3^{\frac{5-1}{4}} \\=3^{\frac{4}{4}} \\=3^1 \\=3$
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.