Question

Express the following in positive exponents only :

$\frac{5^{-2}\times 3^2}{5^{-4}\times 3^{-6}}$

Answer 1

Given that , $\frac{5^{-2}\times 3^2}{5^{-4}\times 3^{-6}}$

$=5^{-2}\times 3^2\times 5^4\times 3^6$ [ Using exponent laws : $a^{-n}=\frac{1}{a^n}$ and $a^n\times a^m=a^{n+m}$ ]

$=5^{-2+4}\times 3^{2+6}$

$=5^2\times 3^8$

Hence , the required expression is $5^2\times 3^8$ .