Linear Algebra Examples

$\sqrt[3]{9} \sqrt[9]{9}$

Step 1

Multiply $\sqrt[3]{9} \sqrt[9]{9}$ .

Tap for more steps...

Step 1.1

Rewrite the expression using the least common index of $9$ .

Tap for more steps...

Step 1.1.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[3]{9}$ as $9^{\frac{1}{3}}$ .

$9^{\frac{1}{3}} \sqrt[9]{9}$

Step 1.1.2

Rewrite $9^{\frac{1}{3}}$ as $9^{\frac{3}{9}}$ .

$9^{\frac{3}{9}} \sqrt[9]{9}$

Step 1.1.3

Rewrite $9^{\frac{3}{9}}$ as $\sqrt[9]{9^{3}}$ .

$\sqrt[9]{9^{3}} \sqrt[9]{9}$

Step 1.2

Combine using the product rule for radicals.

$\sqrt[9]{9^{3} \cdot 9}$

Step 1.3

Multiply $9^{3}$ by $9$ by adding the exponents.

Tap for more steps...

Step 1.3.1

Multiply $9^{3}$ by $9$ .

Tap for more steps...

Step 1.3.1.1

Raise $9$ to the power of $1$ .

$\sqrt[9]{9^{3} \cdot 9^{1}}$

Step 1.3.1.2

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

$\sqrt[9]{9^{3 + 1}}$

Step 1.3.2

Add $3$ and $1$ .

$\sqrt[9]{9^{4}}$

Step 2

Raise $9$ to the power of $4$ .

$\sqrt[9]{6561}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\sqrt[9]{6561}$

Decimal Form:

$2.65526445 \dots$