Question

2 raise to power minus 5 over 4 is to power minus 5 is equal to 2 raise to power 5​

Answer 1

Answer and Explanation:

To prove : 2 raise to power minus 5 over 4 is to power minus 5 is equal to 2 raise to power 5​ ?

Solution :

Taking LHS,

LHS = 2 raise to power minus 5 over 4 is to power minus 5

2 raise to power minus 5 - $2^{-5}$

4 is to power minus 5 - $4^{-5}$

$LHS=\frac{2^{-5}}{4^{-5}}$

Write, $4=2^2$

$LHS=\frac{2^{-5}}{(2^2)^{-5}}$

As $(a^m)^n=a^{mn}$

$LHS=\frac{2^{-5}}{2^2^{-10}}$

As $\frac{a^m}{a^n}=a^{m-n}$

$LHS=2^{-5+10}$

$LHS=2^{5}$

Taking RHS,

RHS = 2 raise to power 5​

$RHS=2^5$

So, LHS=RHS

Hence proved.