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