Simplify fifth root of 5* fifth root of 5^2

$\sqrt[5]{5} \cdot \sqrt[5]{5^{2}}$

Step 1

Combine using the product rule for radicals.

$\sqrt[5]{5 \cdot 5^{2}}$

Step 2

Multiply $5$ by $5^{2}$ by adding the exponents.

Multiply $5$ by $5^{2}$ .

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

$\sqrt[5]{5^{1} \cdot 5^{2}}$

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

$\sqrt[5]{5^{1 + 2}}$

Add $1$ and $2$ .

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

Step 3

Raise $5$ to the power of $3$ .

$\sqrt[5]{125}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\sqrt[5]{125}$

Decimal Form:

$2.62652780 \dots$