Basic Math Examples

${(\sqrt[4]{96 y})}^{18} z^{8}$

Step 1

Rewrite $96 y$ as $2^{4} \cdot (6 y)$ .

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Step 1.1

Factor $16$ out of $96$ .

${\sqrt[4]{16 (6) y}}^{18} z^{8}$

Step 1.2

Rewrite $16$ as $2^{4}$ .

${\sqrt[4]{2^{4} \cdot 6 y}}^{18} z^{8}$

Step 1.3

Add parentheses.

${\sqrt[4]{2^{4} \cdot (6 y)}}^{18} z^{8}$

Step 2

Pull terms out from under the radical.

${(2 \sqrt[4]{6 y})}^{18} z^{8}$

Step 3

Simplify the expression.

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Step 3.1

Apply the product rule to $2 \sqrt[4]{6 y}$ .

$2^{18} {\sqrt[4]{6 y}}^{18} z^{8}$

Step 3.2

Raise $2$ to the power of $18$ .

$262144 {\sqrt[4]{6 y}}^{18} z^{8}$

Step 4

Rewrite ${\sqrt[4]{6 y}}^{18}$ as $\sqrt[4]{{(6 y)}^{18}}$ .

$262144 \sqrt[4]{{(6 y)}^{18}} z^{8}$

Step 5

Apply the product rule to $6 y$ .

$262144 \sqrt[4]{6^{18} y^{18}} z^{8}$

Step 6

Raise $6$ to the power of $18$ .

$262144 \sqrt[4]{101559956668416 y^{18}} z^{8}$

Step 7

Rewrite $101559956668416 y^{18}$ as ${(1296 y^{4})}^{4} \cdot (36 y^{2})$ .

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Step 7.1

Factor $2821109907456$ out of $101559956668416$ .

$262144 \sqrt[4]{2821109907456 (36) y^{18}} z^{8}$

Step 7.2

Rewrite $2821109907456$ as $1296^{4}$ .

$262144 \sqrt[4]{1296^{4} \cdot 36 y^{18}} z^{8}$

Step 7.3

Factor out $y^{16}$ .

$262144 \sqrt[4]{1296^{4} \cdot 36 (y^{16} y^{2})} z^{8}$

Step 7.4

Rewrite $y^{16}$ as ${(y^{4})}^{4}$ .

$262144 \sqrt[4]{1296^{4} \cdot 36 ({(y^{4})}^{4} y^{2})} z^{8}$

Step 7.5

Move $36$ .

$262144 \sqrt[4]{1296^{4} {(y^{4})}^{4} \cdot 36 y^{2}} z^{8}$

Step 7.6

Rewrite $1296^{4} {(y^{4})}^{4}$ as ${(1296 y^{4})}^{4}$ .

$262144 \sqrt[4]{{(1296 y^{4})}^{4} \cdot 36 y^{2}} z^{8}$

Step 7.7

Add parentheses.

$262144 \sqrt[4]{{(1296 y^{4})}^{4} \cdot (36 y^{2})} z^{8}$

Step 8

Pull terms out from under the radical.

$262144 (1296 y^{4} \sqrt[4]{36 y^{2}}) z^{8}$

Step 9

Rewrite $36 y^{2}$ as ${(6 y)}^{2}$ .

$262144 (1296 y^{4} \sqrt[4]{{(6 y)}^{2}}) z^{8}$

Step 10

Rewrite $\sqrt[4]{{(6 y)}^{2}}$ as $\sqrt{\sqrt{{(6 y)}^{2}}}$ .

$262144 (1296 y^{4} \sqrt{\sqrt{{(6 y)}^{2}}}) z^{8}$

Step 11

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

$262144 (1296 y^{4} \sqrt{6 y}) z^{8}$

Step 12

Multiply $1296$ by $262144$ .

$339738624 y^{4} \sqrt{6 y} z^{8}$