The value of 'n' in the following:5 power of-3 ×5 power of n = 5 powe

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