Question

solve for w, where w is a real number.
$w^{\frac{1}{3}} = 3$
if there is more than one solution, separate them with commas.
if there is no solution, click on
o solution\.
$w = \boxed{}$

Explanation:

Step1: Recall the property of exponents

We know that \( w^{\frac{1}{3}} \) is the cube root of \( w \), and to solve for \( w \), we can raise both sides of the equation to the power of 3. The equation is \( w^{\frac{1}{3}} = 3 \).

Step2: Raise both sides to the power of 3

Using the property \((a^m)^n=a^{mn}\), if we raise both sides of \( w^{\frac{1}{3}} = 3 \) to the power of 3, we get \((w^{\frac{1}{3}})^3=3^3\).
Simplifying the left - hand side, \((w^{\frac{1}{3}})^3 = w^{\frac{1}{3}\times3}=w^1 = w\).
Simplifying the right - hand side, \(3^3=27\).

Answer:

\( w = 27 \)