Question

When ${\left(\frac{2}{5}\right)}^4\times {\left(\frac{2}{5}\right)}^{-9}={\left(\frac{2}{5}\right)}^{3m+1}.$ Find the value of $-m.$

Answer 1

Given,

${\left(\frac{2}{5}\right)}^4\times {\left(\frac{2}{5}\right)}^{-9}={\left(\frac{2}{5}\right)}^{3m+1}$

Using rule

$m^p\times m^n=m^{p+n}$

${\left(\frac{2}{5}\right)}^{4+(-9)}={\left(\frac{2}{5}\right)}^{3m+1}$

${\left(\frac{2}{5}\right)}^{-5}={\left(\frac{2}{5}\right)}^{3m+1}$

If bases are same then corresponding powers need to be same.

$3m+1=-5$

$3m=-6$

$m=-2$

So, $-m=2$

Hence correct answer is $2$.