Simplify ((48^(1/4))/(6^(1/4)))^6

${(\frac{48^{\frac{1}{4}}}{6^{\frac{1}{4}}})}^{6}$

Step 1

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

${({(\frac{48}{6})}^{\frac{1}{4}})}^{6}$

Step 2

Multiply the exponents in ${({(\frac{48}{6})}^{\frac{1}{4}})}^{6}$ .

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

${(\frac{48}{6})}^{\frac{1}{4} \cdot 6}$

Cancel the common factor of $2$ .

Factor $2$ out of $4$ .

${(\frac{48}{6})}^{\frac{1}{2 (2)} \cdot 6}$

Factor $2$ out of $6$ .

${(\frac{48}{6})}^{\frac{1}{2 \cdot 2} \cdot (2 \cdot 3)}$

Cancel the common factor.

${(\frac{48}{6})}^{\frac{1}{2 \cdot 2} \cdot (2 \cdot 3)}$

Rewrite the expression.

${(\frac{48}{6})}^{\frac{1}{2} \cdot 3}$

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

${(\frac{48}{6})}^{\frac{3}{2}}$

Step 3

Divide $48$ by $6$ .

$8^{\frac{3}{2}}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$8^{\frac{3}{2}}$

Decimal Form:

$22.62741699 \dots$