Basic Math Examples

$\sqrt{a^{2} \cdot \sqrt{a^{6} \cdot \sqrt{a^{4} \cdot \sqrt{a}}}}$

Step 1

Rewrite $a^{4}$ as ${(a^{2})}^{2}$ .

$\sqrt{a^{2} \sqrt{a^{6} \sqrt{{(a^{2})}^{2} \cdot \sqrt{a}}}}$

Step 2

Pull terms out from under the radical.

$\sqrt{a^{2} \sqrt{a^{6} (a^{2} \sqrt{\sqrt{a}})}}$

Step 3

Rewrite $\sqrt{\sqrt{a}}$ as $\sqrt[4]{a}$ .

$\sqrt{a^{2} \sqrt{a^{6} a^{2} \sqrt[4]{a}}}$

Step 4

Multiply $a^{6}$ by $a^{2}$ by adding the exponents.

Tap for more steps...

Step 4.1

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

$\sqrt{a^{2} \sqrt{a^{6 + 2} \sqrt[4]{a}}}$

Step 4.2

Add $6$ and $2$ .

$\sqrt{a^{2} \sqrt{a^{8} \sqrt[4]{a}}}$

Step 5

Rewrite $a^{8} \sqrt[4]{a}$ as ${({(a^{2})}^{2})}^{2} \sqrt[4]{a}$ .

Tap for more steps...

Step 5.1

Rewrite $a^{8}$ as ${(a^{4})}^{2}$ .

$\sqrt{a^{2} \sqrt{{(a^{4})}^{2} \sqrt[4]{a}}}$

Step 5.2

Rewrite $a^{4}$ as ${(a^{2})}^{2}$ .

$\sqrt{a^{2} \sqrt{{({(a^{2})}^{2})}^{2} \sqrt[4]{a}}}$

Step 6

Pull terms out from under the radical.

$\sqrt{a^{2} ({(a^{2})}^{2} \sqrt{\sqrt[4]{a}})}$

Step 7

Multiply the exponents in ${(a^{2})}^{2}$ .

Tap for more steps...

Step 7.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\sqrt{a^{2} (a^{2 \cdot 2} \sqrt{\sqrt[4]{a}})}$

Step 7.2

Multiply $2$ by $2$ .

$\sqrt{a^{2} (a^{4} \sqrt{\sqrt[4]{a}})}$

Step 8

Rewrite $\sqrt{\sqrt[4]{a}}$ as $\sqrt[8]{a}$ .

$\sqrt{a^{2} a^{4} \sqrt[8]{a}}$

Step 9

Multiply $a^{2}$ by $a^{4}$ by adding the exponents.

Tap for more steps...

Step 9.1

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

$\sqrt{a^{2 + 4} \sqrt[8]{a}}$

Step 9.2

Add $2$ and $4$ .

$\sqrt{a^{6} \sqrt[8]{a}}$

Step 10

Rewrite $a^{6}$ as ${(a^{3})}^{2}$ .

$\sqrt{{(a^{3})}^{2} \sqrt[8]{a}}$

Step 11

Pull terms out from under the radical.

$a^{3} \sqrt{\sqrt[8]{a}}$

Step 12

Rewrite $\sqrt{\sqrt[8]{a}}$ as $\sqrt[16]{a}$ .

$a^{3} \sqrt[16]{a}$