Convert to Radical Form (5^(1/8)*5^(3/8))^3

${(5^{\frac{1}{8}} \cdot 5^{\frac{3}{8}})}^{3}$

Step 1

Multiply $5^{\frac{1}{8}}$ by $5^{\frac{3}{8}}$ by adding the exponents.

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

${(5^{\frac{1}{8} + \frac{3}{8}})}^{3}$

Combine the numerators over the common denominator.

${(5^{\frac{1 + 3}{8}})}^{3}$

Add $1$ and $3$ .

${(5^{\frac{4}{8}})}^{3}$

Cancel the common factor of $4$ and $8$ .

Factor $4$ out of $4$ .

${(5^{\frac{4 (1)}{8}})}^{3}$

Cancel the common factors.

Factor $4$ out of $8$ .

${(5^{\frac{4 \cdot 1}{4 \cdot 2}})}^{3}$

Cancel the common factor.

${(5^{\frac{4 \cdot 1}{4 \cdot 2}})}^{3}$

Rewrite the expression.

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

Step 2

Apply the rule $x^{\frac{m}{n}} = \sqrt[n]{x^{m}}$ to rewrite the exponentiation as a radical.

${\sqrt{5^{1}}}^{3}$

Step 3

Anything raised to $1$ is the base itself.

${\sqrt{5}}^{3}$

Step 4

The result can be shown in multiple forms.

Exact Form:

${\sqrt{5}}^{3}$

Decimal Form:

$11.18033988 \dots$