Powers with negative and rational exponents

Text

Evaluate without a calculator:

• (a) $5^{-2}$ (write it as a fraction)
• (b) $27^{1/3}$
• (c) $16^{3/4}$
• (d) $81^{-1/2}$

Solution

(a) $5^{-2}=\dfrac{1}{5^{2}}=\dfrac{1}{25}=0.04$. (b) $27^{1/3}=\sqrt[3]{27}=3$. (c) $16^{3/4}=\left(\sqrt[4]{16}\right)^{3}=2^{3}=8$. (d) $81^{-1/2}=\dfrac{1}{\sqrt{81}}=\dfrac{1}{9}\approx 0.111$.

$\boxed{\;(a)\;\tfrac{1}{25}\qquad (b)\;3\qquad (c)\;8\qquad (d)\;\tfrac{1}{9}\;}$