Questions: (42^(1/3) / 6^(1/3))^2

Solution Steps

The given expression is: \[ \left(\frac{42^{\frac{1}{3}}}{6^{\frac{1}{3}}}\right)^{2} \] We can rewrite the fraction as: \[ \frac{42^{\frac{1}{3}}}{6^{\frac{1}{3}}} = \left(\frac{42}{6}\right)^{\frac{1}{3}} \] Simplify \(\frac{42}{6}\): \[ \frac{42}{6} = 7 \] So the expression becomes: \[ \left(7^{\frac{1}{3}}\right)^{2} \]

Using the exponent rule \((a^m)^n = a^{m \cdot n}\), we simplify: \[ \left(7^{\frac{1}{3}}\right)^{2} = 7^{\frac{2}{3}} \]

The expression \(7^{\frac{2}{3}}\) is already in its simplest form.

Final Answer