Algebra Examples

$\sqrt{7} \cdot \sqrt[5]{7^{6}}$

Step 1

Raise $7$ to the power of $6$ .

$\sqrt{7} \cdot \sqrt[5]{117649}$

Step 2

Rewrite $117649$ as $7^{5} \cdot 7$ .

Tap for more steps...

Step 2.1

Factor $16807$ out of $117649$ .

$\sqrt{7} \cdot \sqrt[5]{16807 (7)}$

Step 2.2

Rewrite $16807$ as $7^{5}$ .

$\sqrt{7} \cdot \sqrt[5]{7^{5} \cdot 7}$

Step 3

Pull terms out from under the radical.

$\sqrt{7} \cdot (7 \sqrt[5]{7})$

Step 4

Multiply $\sqrt{7} (7 \sqrt[5]{7})$ .

Tap for more steps...

Step 4.1

Rewrite the expression using the least common index of $10$ .

Tap for more steps...

Step 4.1.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{7}$ as $7^{\frac{1}{2}}$ .

$7 (7^{\frac{1}{2}} \sqrt[5]{7})$

Step 4.1.2

Rewrite $7^{\frac{1}{2}}$ as $7^{\frac{5}{10}}$ .

$7 (7^{\frac{5}{10}} \sqrt[5]{7})$

Step 4.1.3

Rewrite $7^{\frac{5}{10}}$ as $\sqrt[10]{7^{5}}$ .

$7 (\sqrt[10]{7^{5}} \sqrt[5]{7})$

Step 4.1.4

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[5]{7}$ as $7^{\frac{1}{5}}$ .

$7 (\sqrt[10]{7^{5}} \cdot 7^{\frac{1}{5}})$

Step 4.1.5

Rewrite $7^{\frac{1}{5}}$ as $7^{\frac{2}{10}}$ .

$7 (\sqrt[10]{7^{5}} \cdot 7^{\frac{2}{10}})$

Step 4.1.6

Rewrite $7^{\frac{2}{10}}$ as $\sqrt[10]{7^{2}}$ .

$7 (\sqrt[10]{7^{5}} \sqrt[10]{7^{2}})$

Step 4.2

Combine using the product rule for radicals.

$7 \sqrt[10]{7^{5} \cdot 7^{2}}$

Step 4.3

Multiply $7^{5}$ by $7^{2}$ by adding the exponents.

Tap for more steps...

Step 4.3.1

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

$7 \sqrt[10]{7^{5 + 2}}$

Step 4.3.2

Add $5$ and $2$ .

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

Step 5

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

$7 \sqrt[10]{823543}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$7 \sqrt[10]{823543}$

Decimal Form:

$27.33170143 \dots$