Math, asked by princess2264, 10 months ago

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

Answers

Answered by pinquancaro
2

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.

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