Simplify cube root of 10^5* cube root of 10^2

$\sqrt[3]{10^{5}} \cdot \sqrt[3]{10^{2}}$

Step 1

Combine using the product rule for radicals.

$\sqrt[3]{10^{5} \cdot 10^{2}}$

Step 2

Multiply $10^{5}$ by $10^{2}$ by adding the exponents.

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

$\sqrt[3]{10^{5 + 2}}$

Add $5$ and $2$ .

$\sqrt[3]{10^{7}}$

Step 3

Raise $10$ to the power of $7$ .

$\sqrt[3]{10000000}$

Step 4

Rewrite $10000000$ as $100^{3} \cdot 10$ .

Factor $1000000$ out of $10000000$ .

$\sqrt[3]{1000000 (10)}$

Rewrite $1000000$ as $100^{3}$ .

$\sqrt[3]{100^{3} \cdot 10}$

Step 5

Pull terms out from under the radical.

$100 \sqrt[3]{10}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$100 \sqrt[3]{10}$

Decimal Form:

$215.44346900 \dots$