Simplify cube root of 5^5* cube root of 5

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

Step 1

Combine using the product rule for radicals.

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

Step 2

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

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

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

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

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

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

Add $5$ and $1$ .

$\sqrt[3]{5^{6}}$

Step 3

Raise $5$ to the power of $6$ .

$\sqrt[3]{15625}$

Step 4

Rewrite $15625$ as $25^{3}$ .

$\sqrt[3]{25^{3}}$

Step 5

Pull terms out from under the radical, assuming real numbers.

$25$