Simplify ((42^(1/3))/(6^(1/3)))^2

${(\frac{42^{\frac{1}{3}}}{6^{\frac{1}{3}}})}^{2}$

Use the power of quotient rule $\frac{a^{m}}{b^{m}} = {(\frac{a}{b})}^{m}$ .

${({(\frac{42}{6})}^{\frac{1}{3}})}^{2}$

Multiply the exponents in ${({(\frac{42}{6})}^{\frac{1}{3}})}^{2}$ .

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

${(\frac{42}{6})}^{\frac{1}{3} \cdot 2}$

Combine $\frac{1}{3}$ and $2$ .

${(\frac{42}{6})}^{\frac{2}{3}}$

Divide $42$ by $6$ .

$7^{\frac{2}{3}}$

The result can be shown in multiple forms.

Exact Form:

$7^{\frac{2}{3}}$

Decimal Form:

$3.65930571 \dots$