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

$(4^{-7}$÷ $4^{-10})\times 4^{-5}$

$\left(\frac{4^{-7}}{4^{-10}}\right)\times 4^{-5}$

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

$\because a^m\times a^n=(a{)}^{m+n}$

$\Rightarrow 4^{3-5}$
$=4^{-2}$
$=\frac{1}{16}$
$={16}^{-1}$