Algebra Examples

$\sqrt[5]{10} \cdot \sqrt[5]{10^{2}}$

Step 1

Combine using the product rule for radicals.

$\sqrt[5]{10 \cdot 10^{2}}$

Step 2

Rewrite $10 \cdot 10^{2}$ as $1000 \cdot 10^{0}$ .

$\sqrt[5]{1000 \cdot 10^{0}}$

Step 3

Rewrite $\sqrt[5]{1000 \cdot 10^{0}}$ as $\sqrt[5]{1000} \cdot \sqrt[5]{10^{0}}$ .

$\sqrt[5]{1000} \cdot \sqrt[5]{10^{0}}$

Step 4

Evaluate the root.

$3.9810717 \cdot \sqrt[5]{10^{0}}$

Step 5

Rewrite $10^{0}$ as ${(10^{0})}^{5}$ .

$3.9810717 \cdot \sqrt[5]{{(10^{0})}^{5}}$

Step 6

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

$3.9810717 \cdot 10^{0}$

Step 7

Convert $3.9810717 \cdot 10^{0}$ from scientific notation.

$3.9810717$