if $(-3)^{-5}=\frac{1}{x}$, what is the value of $x$?\n-243\n$-\frac{1}{243}$\n$\frac{1}{243}$\n243
if $(-3)^{-5}=\frac{1}{x}$, what is the value of $x$?\n-243\n$-\frac{1}{243}$\n$\frac{1}{243}$\n243
Answer
Answer:
A. -243
Explanation:
Step1: Use negative exponent rule
The negative exponent rule states that (a^{-n}=\frac{1}{a^{n}}). So, ((-3)^{-5}=\frac{1}{(-3)^{5}}).
Step2: Calculate ((-3)^{5})
((-3)^{5}=(-3)\times(-3)\times(-3)\times(-3)\times(-3)). First, ((-3)\times(-3) = 9), then (9\times(-3)=-27), (-27\times(-3) = 81), (81\times(-3)=-243). So, ((-3)^{5}=-243). Since ((-3)^{-5}=\frac{1}{x}) and ((-3)^{-5}=\frac{1}{(-3)^{5}}), then (x = (-3)^{5}=-243).