Question

(3³)² × 3⁵ =
_________
3¹³ =

Answer 1

$(x^a)^b=x^{a*b} \\x^a+x^b=x^{a+b} \\ \frac{x^a}{x^b}=x^{a-b} \\x^{-a}= \frac{1}{x^{a}} \\ \\ \\ \frac{(3^3)^2*3^5}{3^{13}} = \frac{3^{3*2}*3^5}{3^{13}} = \frac{3^{6}*3^5}{3^{13}} = \frac{3^{6+5}}{3^{13}} =\frac{3^{11}}{3^{13}} =3^{11-13}=3^{-2}= \\ = \frac{1}{3^{2}} = \frac{1}{9}$