Prove that:

$\frac{a^{-1}}{a^{-1}+b^{-1}}+\frac{a^{-1}}{a^{-1}-b^{-1}}=\frac{2b^2}{b^2-a^2}$

If $a, m \mathrm{and} n$ are rational numbers, then $a^m\times a^n=a^p$. Then the value of $p=$_____.

Evaluate $3^{-4}$

$\left(3^{-1}+2^{-1}\right)\times 5^{-2}=$ 

Evaluate ${\left\{{\left(\frac{-2}{3}\right)}^3\right\}}^{-2}$.

Simplify $\left(3^{-1}+6^{-1}\right) ÷ {\left(\frac{3}{4}\right)}^{-1}$

Simplify the following:

Find the value of $3^{45}\times 3^{25}-3^{28}\times 3^{42}$.

By what number should ${\left(\frac{-2}{3}\right)}^{-3}$ be divided so that the quotient is ${\left(\frac{4}{9}\right)}^{-2}$?