Question

5. In the property of indices a^m ÷ a^n = a^m-n, taking m=n
show that a^-n=1÷a^n
​

Answer 1

$\dag \: \mathcal{ \huge{ \green{Solution }}} \: \dag$

$\longrightarrow \: {a}^{m} \div {a}^{n} = {a}^{m - n}$

$\dag \: \mathcal{ \huge{ \green{Proof}}} \: \dag$

$\longrightarrow \tt \: \: \underline{LHS}$

$\longrightarrow {a}^{ - n}$

$\longrightarrow {a}^{0 - n}$

$\longrightarrow \frac{ {a}^{0} }{ {a}^{n} }$

$\longrightarrow \bf \: \frac{1}{ {a}^{n} }$

$\longrightarrow \tt \: \: \underline{RHS} \: \: \: \: \: \: \: \bf \red{ [Proved]}$