Question

Question 91

Solve the following.
$\left(i\right){100}^{-10}\left(ii\right)2^{-2}\times 2^{-3}\left(iii\right){\left(\frac{1}{2}\right)}^{-2}÷{\left(\frac{1}{2}\right)}^{-3}$

Answer 1

(i) ${100}^{-10}={\left(\frac{1}{100}\right)}^{10}$
(ii) $2^{-2}\times 2^{-3}$
$=2^{-2-3}=2^{-5}$
$={\left(\frac{1}{2}\right)}^5=\frac{1}{32}$
(iii) ${\left(\frac{1}{2}\right)}^{-2}÷{\left(\frac{1}{2}\right)}^{-3}$
$={\left(\frac{1}{2}\right)}^{-2+3}={\left(\frac{1}{2}\right)}^1=\frac{1}{2}$