Question

3^2m × 3^-3 = 3^5 then m is equal to​

Answer 1

Laws of exponents.

$\begin{gathered}\boxed{\begin{minipage}{5 cm}\bf{\dag}\:\:\underline{\text{Law of Exponents :}}\\\\\bigstar\:\:\sf\dfrac{a^m}{a^n} = a^{m - n}\\\\\bigstar\:\:\sf{(a^m)^n = a^{mn}}\\\\\bigstar\:\:\sf(a^m)(a^n) = a^{m + n}\\\\\bigstar\:\:\sf\dfrac{1}{a^n} = a^{-n}\\\\\bigstar\:\:\sf\sqrt[\sf n]{\sf a} = (a)^{\dfrac{1}{n}}\end{minipage}}\end{gathered}$

$\large\mathfrak \pink{Solution:-}$

$\underline \mathbb{BY \: THE \: PROBLEM:-}$

${3}^{2m} \times {3}^{ - 3} = {3}^{5} \\ \\ \implies \: {3}^{2m + ( - 3)} = {3}^{5} \\ \\ \implies \: {3}^{2m - 3} = {3}^{5} \\ \\ \implies \:2m - 3 = 5\\ \\ \implies \:2m = 5 + 3\\ \\ \implies \:2m = 8\\ \\ \implies \:m = \frac{8}{2} \\ \\ \implies \:m = 4$