Question

The value of 'n' in the
following:
5 power of-3 ×5 power of n = 5 power of 4
ک
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Answer 1

Given :

$\sf \large {5}^{ - 3} \times {5}^{n} = {5}^{4}$

To find :

• the value of n

Solution :

$\sf \implies {5}^{ - 3} \times {5}^{n} = {5}^{4}$

We know that :-

$\underline { \boxed{ \large \bf{a}^{ p} \times {a}^{q} = {a}^{p + q} }}$

$\sf \implies {5}^{ - 3 + n} = {5}^{4}$

Now comparing both sides.

$\sf \implies { - 3 + n} = {4}$

$\sf \implies { n} = {4} + 3$

$\sf \implies { n} = 7$

Answer :

• Value of n = 7

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Verification of answer :-

To verify the answer put n = 7 in :-

$\sf {5}^{ - 3} \times {5}^{n} = {5}^{4}$

If we get RHS = LHS then our answer is correct.

RHS = 5⁴

LHS :-

$\implies\sf {5}^{ - 3} \times {5}^{7} = ({5})^{ - 3 + 7}$

$\implies\sf ({5})^{ - 3 + 7} = {5}^{4}$

Therefore LHS = RHS

hence verified