Question

Find the value of $m$ if $(2{)}^2\times (-5{)}^4={50}^m.$

• A. -2
• B. 2
• C. -4
• D. 4

Answer 1

The correct option is B 2

Consider the equation $2^2\times (-5{)}^4={50}^m.$
Since $(a^m{)}^n=a^{mn},$
$2^2\times \left(\right(-5{)}^2{)}^2={50}^m$
$⟹2^2\times {25}^2={50}^m$
$⟹{50}^2={50}^m(\because a^m\times b^m=(ab{)}^m)$
$⟹m=2(a^m=a^n⟹m=n\text{for}a\ne 0,-1,1)$