Evaluate fifth root of 5^3* fifth root of 5

$\sqrt[5]{5^{3}} \cdot \sqrt[5]{5}$

Step 1

Combine using the product rule for radicals.

$\sqrt[5]{5^{3} \cdot 5}$

Step 2

Multiply $5^{3}$ by $5$ by adding the exponents.

Multiply $5^{3}$ by $5$ .

Raise $5$ to the power of $1$ .

$\sqrt[5]{5^{3} \cdot 5^{1}}$

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

$\sqrt[5]{5^{3 + 1}}$

Add $3$ and $1$ .

$\sqrt[5]{5^{4}}$

Step 3

Raise $5$ to the power of $4$ .

$\sqrt[5]{625}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\sqrt[5]{625}$

Decimal Form:

$3.62389831 \dots$