Basic Math Examples

$- 4^{4 \sqrt{y^{7}} + 6 \sqrt{81 y^{7}} - y^{4} + \sqrt{y^{3}}}$

Step 1

Simplify each term.

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Step 1.1

Rewrite $y^{7}$ as ${(y^{3})}^{2} y$ .

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Step 1.1.1

Factor out $y^{6}$ .

$- 4^{4 \sqrt{y^{6} y} + 6 \sqrt{81 y^{7}} - y^{4} + \sqrt{y^{3}}}$

Step 1.1.2

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

$- 4^{4 \sqrt{{(y^{3})}^{2} y} + 6 \sqrt{81 y^{7}} - y^{4} + \sqrt{y^{3}}}$

Step 1.2

Pull terms out from under the radical.

$- 4^{4 (y^{3} \sqrt{y}) + 6 \sqrt{81 y^{7}} - y^{4} + \sqrt{y^{3}}}$

Step 1.3

Rewrite $81 y^{7}$ as ${(9 y^{3})}^{2} y$ .

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Step 1.3.1

Rewrite $81$ as $9^{2}$ .

$- 4^{4 y^{3} \sqrt{y} + 6 \sqrt{9^{2} y^{7}} - y^{4} + \sqrt{y^{3}}}$

Step 1.3.2

Factor out $y^{6}$ .

$- 4^{4 y^{3} \sqrt{y} + 6 \sqrt{9^{2} (y^{6} y)} - y^{4} + \sqrt{y^{3}}}$

Step 1.3.3

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

$- 4^{4 y^{3} \sqrt{y} + 6 \sqrt{9^{2} ({(y^{3})}^{2} y)} - y^{4} + \sqrt{y^{3}}}$

Step 1.3.4

Rewrite $9^{2} {(y^{3})}^{2}$ as ${(9 y^{3})}^{2}$ .

$- 4^{4 y^{3} \sqrt{y} + 6 \sqrt{{(9 y^{3})}^{2} y} - y^{4} + \sqrt{y^{3}}}$

Step 1.4

Pull terms out from under the radical.

$- 4^{4 y^{3} \sqrt{y} + 6 (9 y^{3} \sqrt{y}) - y^{4} + \sqrt{y^{3}}}$

Step 1.5

Multiply $9$ by $6$ .

$- 4^{4 y^{3} \sqrt{y} + 54 (y^{3} \sqrt{y}) - y^{4} + \sqrt{y^{3}}}$

Step 1.6

Factor out $y^{2}$ .

$- 4^{4 y^{3} \sqrt{y} + 54 y^{3} \sqrt{y} - y^{4} + \sqrt{y^{2} y}}$

Step 1.7

Pull terms out from under the radical.

$- 4^{4 y^{3} \sqrt{y} + 54 y^{3} \sqrt{y} - y^{4} + y \sqrt{y}}$

Step 2

Add $4 y^{3} \sqrt{y}$ and $54 y^{3} \sqrt{y}$ .

$- 4^{58 y^{3} \sqrt{y} - y^{4} + y \sqrt{y}}$