Evaluate cube root of 7^4* cube root of 7^4

$\sqrt[3]{7^{4}} \cdot \sqrt[3]{7^{4}}$

Step 1

Combine using the product rule for radicals.

$\sqrt[3]{7^{4} \cdot 7^{4}}$

Step 2

Multiply $7^{4}$ by $7^{4}$ by adding the exponents.

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

$\sqrt[3]{7^{4 + 4}}$

Add $4$ and $4$ .

$\sqrt[3]{7^{8}}$

Step 3

Raise $7$ to the power of $8$ .

$\sqrt[3]{5764801}$

Step 4

Rewrite $5764801$ as $49^{3} \cdot 49$ .

Factor $117649$ out of $5764801$ .

$\sqrt[3]{117649 (49)}$

Rewrite $117649$ as $49^{3}$ .

$\sqrt[3]{49^{3} \cdot 49}$

Step 5

Pull terms out from under the radical.

$49 \sqrt[3]{49}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$49 \sqrt[3]{49}$

Decimal Form:

$179.30597979 \dots$