Question: Simplify. \[ \left( w^2 \right)^{\frac{7}{6}} \] Write your answer without parentheses…

Simplify.

\[ \left( w^2 \right)^{\frac{7}{6}} \]

Write your answer without parentheses. Assume that the variable represents a positive real number.

Solution

The problem is to simplify the expression \(\left(w^2\right)^{\frac{7}{6}}\). First, apply the power of a power property of exponents, which states that \((a^m)^n = a^{m \cdot n}\). \[ \left(w^2\right)^{\frac{7}{6}} = w^{2 \cdot \frac{7}{6}} \] Now, perform the multiplication in the exponent: \[ 2 \cdot \frac{7}{6} = \frac{14}{6} = \frac{7}{3} \] So, the expression simplifies to: \[ w^{\frac{7}{3}} \] The answer is \(w^{\frac{7}{3}}\).