Question

Evaluate (i) (3${}^0+2^{-1}$)$\times$$4^2$
(ii) (2${}^{-1}\times 4^{-2})÷2^{-3}$
(iii) $(\frac{5}{8}{)}^7\times (\frac{8}{5}{)}^{-5}$

Answer 1

$i\left)\right(3^0+2^{-1})\times 4^2$

$=(1+\frac{1}{2})\times 16=3\times 16=24$

$\left(ii\right)(2^{-1}+4^{-2})÷2^{-3}$

$=(\frac{1}{2}+\frac{1}{6})÷\left(\frac{1}{8}\right)$

$=\frac{\frac{9}{16}}{\frac{1}{8}}=\frac{9}{16}\times 8=\frac{9}{2}-4.5$

(iii) $(\frac{5}{8}{)}^7\times (\frac{8}{5}{)}^{-5}$

$=(\frac{5}{8}{)}^7\times (\frac{5}{8}{)}^5=(\frac{5}{8}{)}^{12}$