Evaluate square root of 7^3* square root of 7

$\sqrt{7^{3}} \cdot \sqrt{7}$

Step 1

Combine using the product rule for radicals.

$\sqrt{7^{3} \cdot 7}$

Step 2

Multiply $7^{3}$ by $7$ by adding the exponents.

Multiply $7^{3}$ by $7$ .

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

$\sqrt{7^{3} \cdot 7^{1}}$

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

$\sqrt{7^{3 + 1}}$

Add $3$ and $1$ .

$\sqrt{7^{4}}$

Step 3

Raise $7$ to the power of $4$ .

$\sqrt{2401}$

Step 4

Rewrite $2401$ as $49^{2}$ .

$\sqrt{49^{2}}$

Step 5

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

$49$