Question

By what number should we multiply $4^{-3}$ so that the product may be equal to 64?

• A. $4^5$
• B. $2^{12}$
• C. $2^6$
• D. $2^{1}0$

Answer 1

The correct option is B

$2^{12}$

Let, the required number be $x$

$\Rightarrow x\times 4^{-3}=64$
$\Rightarrow x\times \frac{1}{4^3}=64$ ($\because a^{(-m)}=\frac{1}{a^m}$)
$\Rightarrow x=64\times 4^3=2^6\times (2^2{)}^3=2^6\times 2^6$

$=2^{12}$ ($\because a^m\times a^n=(a{)}^{m+n}$)

$\therefore valueofxis{2}^{12}$