Question

If $\frac{2^m\times 2^4\times 2^{-6}}{2^{-5}}=2^{10}$, then $m$ = ___.

• A. -3
• B. 7
• C. 10
• D. 17

Answer 1

The correct option is B 7

For integers $a,m$ and $n$, $a\ne 0$ we have
$a^m\times a^n=a^{m+n}\text{and}{a}^{-m}=\frac{1}{a^m}.$

Given that $\frac{2^m\times 2^4\times 2^{-6}}{2^{-5}}=2^{10}.$
$⟹2^m\times 2^4\times 2^{-6}\times 2^5=2^{10}$
$⟹2^m\times 2^{[4+(-6)+5]}=2^{10}[\because a^m\times a^n=a^{m+n}]$
$⟹2^m\times 2^3=2^{10}⟹2^{m+3}=2^{10}[\because a^m\times a^n=a^{m+n}]$

Since the bases are the same on both sides of the equation, we can equate the exponents.
$⟹m+3=10$
$⟹m=7$