Question

What is the value of the expression 1/3^-5? a. 243 b. 15 c. 1/15 d. 1/243

Answer 1

$a^{-n}=\left(\dfrac{1}{a}\right)^n\\-------------------\\\left(\dfrac{1}{3}\right)^{-5}=\left(\dfrac{3}{1}\right)^5=3^5=3\cdot3\cdot3\cdot3\cdot3=\huge\boxed{243}\leftarrow \boxed{a}$

$If\ the\ expression\ is\ \dfrac{1}{3^{-5}}\ therefore\ is\ the\ same\ \dfrac{1}{\dfrac{1}{3^5}}=3^5=\huge\boxed{243}$

Answer 2

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

So,
$\frac {1}{3^{-5}}=3^5= 3 \times 3 \times 3 \ times 3 \times 3 = 243$