Question

1. Which expression is equivalent to 60m 2n6 for all values of m and n where the 5m-on-2 expression is defined? A. 12mns 12n B D. 55m?n mo​

Answer 1

Given:

The expression is:

$\dfrac{60m^{-2}n^6}{5m^{-4}n^{-2}}$

To find:

The equivalent expression.

Solution:

We have,

$\dfrac{60m^{-2}n^6}{5m^{-4}n^{-2}}$

It can be written as:

$=\dfrac{60}{5}\times \dfrac{m^{-2}}{m^{-4}}\times \dfrac{n^6}{n^{-2}}$

$=12\times m^{-2-(-4)}\times n^{6-(-2)}$             $[\because \dfrac{a^m}{a^n}=a^{m-n}]$

$=12\times m^{-2+4}\times n^{6+2}$

$=12m^{2}n^{8}$

Therefore, the correct option is A.