Simplify ((20^(1/2))/(5^(1/2)))^3

${(\frac{20^{\frac{1}{2}}}{5^{\frac{1}{2}}})}^{3}$

Step 1

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

${({(\frac{20}{5})}^{\frac{1}{2}})}^{3}$

Step 2

Simplify the expression.

Multiply the exponents in ${({(\frac{20}{5})}^{\frac{1}{2}})}^{3}$ .

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

${(\frac{20}{5})}^{\frac{1}{2} \cdot 3}$

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

${(\frac{20}{5})}^{\frac{3}{2}}$

Divide $20$ by $5$ .

$4^{\frac{3}{2}}$

Rewrite $4$ as $2^{2}$ .

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

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

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

Step 3

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

$2^{3}$

Step 4

Raise $2$ to the power of $3$ .

$8$