Question

5 (3^5 = 243)
a. use this equation to write an expression equivalent to 3 using a root.
b. use this equation to write an expression equivalent to 3 using an exponent.

Explanation:

Step1: Isolate 3 via root operation

Take 5th root of both sides:
$$\sqrt[5]{3^5} = \sqrt[5]{243}$$
Simplify left side: $3 = \sqrt[5]{243}$

Step2: Isolate 3 via exponent operation

Take $\frac{1}{5}$ power of both sides:
$$(3^5)^{\frac{1}{5}} = 243^{\frac{1}{5}}$$
Simplify left side: $3 = 243^{\frac{1}{5}}$

Answer:

a. $\sqrt[5]{243}$
b. $243^{\frac{1}{5}}$