Question

The value of ($4^{-7}$ ÷ $4^{-10}$ ) × $4^{-5}$ is ${16}^{-1}$.

• A. True
• B. False

Answer 1

The correct option is A

True

The value of ($4^{-7}$ ÷ $4^{-10}$ ) × $4^{-5}$ is ${16}^{-1}$.
$(4^{-7}$÷ $4^{-10})\times 4^{-5}$

=$\left(\frac{4^{-7}}{4^{-10}}\right)\times 4^{-5}$
=$4^{-7+10}\times 4^{-5}(\because \frac{a^m}{a^n}=a^{m-n})$
$=4^3\times 4^{-5}$
$\Rightarrow 4^{3-5}(\because a^m\times a^n=a^{m+n})$
$=4^{-2}=\frac{1}{4^2}$
$=\frac{1}{16}$
$={16}^{-1}$