Simplify fifth root of 7* fifth root of 7^6

$\sqrt[5]{7} \cdot \sqrt[5]{7^{6}}$

Step 1

Combine using the product rule for radicals.

$\sqrt[5]{7 \cdot 7^{6}}$

Step 2

Multiply $7$ by $7^{6}$ by adding the exponents.

Multiply $7$ by $7^{6}$ .

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

$\sqrt[5]{7^{1} \cdot 7^{6}}$

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

$\sqrt[5]{7^{1 + 6}}$

Add $1$ and $6$ .

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

Step 3

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

$\sqrt[5]{823543}$

Step 4

Rewrite $823543$ as $7^{5} \cdot 49$ .

Factor $16807$ out of $823543$ .

$\sqrt[5]{16807 (49)}$

Rewrite $16807$ as $7^{5}$ .

$\sqrt[5]{7^{5} \cdot 49}$

Step 5

Pull terms out from under the radical.

$7 \sqrt[5]{49}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$7 \sqrt[5]{49}$

Decimal Form:

$15.24534497 \dots$