Evaluate fifth root of 3^3* fifth root of 3^4

$\sqrt[5]{3^{3}} \cdot \sqrt[5]{3^{4}}$

Combine using the product rule for radicals.

$\sqrt[5]{3^{3} \cdot 3^{4}}$

Multiply $3^{3}$ by $3^{4}$ by adding the exponents.

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

$\sqrt[5]{3^{3 + 4}}$

Add $3$ and $4$ .

$\sqrt[5]{3^{7}}$

Raise $3$ to the power of $7$ .

$\sqrt[5]{2187}$

Rewrite $2187$ as $3^{5} \cdot 9$ .

Factor $243$ out of $2187$ .

$\sqrt[5]{243 (9)}$

Rewrite $243$ as $3^{5}$ .

$\sqrt[5]{3^{5} \cdot 9}$

Pull terms out from under the radical.

$3 \sqrt[5]{9}$

The result can be shown in multiple forms.

Exact Form:

$3 \sqrt[5]{9}$

Decimal Form:

$4.65553672 \dots$