Simplify fifth root of 7* fifth root of 7^2

$\sqrt[5]{7} \cdot \sqrt[5]{7^{2}}$

Step 1

Combine using the product rule for radicals.

$\sqrt[5]{7 \cdot 7^{2}}$

Step 2

Multiply $7$ by $7^{2}$ by adding the exponents.

Multiply $7$ by $7^{2}$ .

Raise $7$ to the power of $1$ .

$\sqrt[5]{7^{1} \cdot 7^{2}}$

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

$\sqrt[5]{7^{1 + 2}}$

Add $1$ and $2$ .

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

Step 3

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

$\sqrt[5]{343}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\sqrt[5]{343}$

Decimal Form:

$3.21409584 \dots$