Question

Simplify:
$(3^{-7}\times 3^{-10})\times 3^{-5}$.

Answer 1

To simplify: $(3^{-7}\times 3^{-10})\times 3^{-5}$

$(3^{-7}\times 3^{-10})\times 3^{-5}$

$=3^{-7+(-10)}\times 3^{-5}$ [$\because a^m\times a^n=a^{m+n}$]

$=3^{-7-10}\times 3^{-5}$

$=3^{-17}\times 3^{-5}$

$=3^{-17+(-5)}$

$=3^{-17-5}$

$=3^{-22}$

$=\frac{1}{3^{22}}$ [$\because a^{-m}=\frac{1}{a^m},a\ne 0$]

$\therefore (3^{-7}\times 3^{-10})\times 3^{-5}=\frac{1}{3^{22}}$