Calculus with Applications (10th Edition)

Published by Pearson
ISBN 10: 0321749006
ISBN 13: 978-0-32174-900-0

Prerequisite Skills Diagnostic Test: 21

Answer

$$\frac{2}{p^2q}$$

Work Step by Step

An expression raised to a negative exponent is equivalent to the reciprocal of the expression to that same positive exponent $$a^{-b}=\frac{1}{a^b}$$ so $$\frac{4^{1/4}(p^{2/3}q^{-1/3})^{-1}}{4^{-1/4}p^{4/3}q^{4/3}}=\frac{4^{1/4}4^{1/4}q^{1/3}}{p^{2/3}p^{4/3}q^{4/3}}$$ Add exponents when multiplying powers of the same base and subtract when dividing powers of the same base $$=\frac{4^{(1/4+1/4)}}{p^{(2/3+4/3)}q^{(4/3-1/3)}}=\frac{2}{p^2q}$$
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