Question

If $5^{-x}=3$, what does $5^{3x}$ equals?

Answer 1

Solve the given equation $5^{-x}=3$ by using the exponent rule:

$\begin{array}{rcl}{5}^{-x}& =& 3\\ & \Rightarrow & \frac{1}{5^x}=3\\ & \Rightarrow & 5^x=\frac{1}{3}\end{array}$

Since $5^x=\frac{1}{3}$ then:

$\begin{array}{rcl}{5}^{3x}& =& {\left(5^x\right)}^3\\ & =& {\left(\frac{1}{3}\right)}^3\left[5^x=\frac{1}{3}\right]\\ & =& \frac{1}{27}\end{array}$

Thus, the value of $5^{3x}$ is equal to $\frac{1}{27}$.