Answer
(a) $81$
(b) $-81$
(c) $\dfrac{1}{81}$
(d) $25$
(e) $\dfrac{9}{4}$
(f) $\dfrac{1}{8}$
Work Step by Step
(a)
$(-3)^4=(-3)(-3)(-3)(-3)=81$
(b)
$-3^4=-(3)(3)(3)(3)=-81$
(c)
$3^{-4} = \dfrac{1}{3^4} = \dfrac{1}{81}$
(d)
$\dfrac{5^{23}}{5^{21}}=5^{23-21}=5^2=25$
(e)
$\left(\frac{2}{3}\right)^2=\dfrac{1}{\left(\frac{2}{3}\right)^2}=\dfrac{1}{\frac{4}{9}}=1 \cdot \dfrac{9}{4}=\dfrac{9}{4}$
(f)
$16^{-\frac{3}{4}}=\dfrac{1}{16^{\frac{3}{4}}}=\dfrac{1}{\sqrt[4]{16^3}}=\dfrac{1}{\sqrt[4]{(2^4)^3}}=\dfrac{1}{2^3}=\dfrac{1}{8}$
