Precalculus Examples

$4 {(\sqrt{64})}^{3} y^{8} \cdot (4 \sqrt{121 h})$

Step 1

Simplify the expression.

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Step 1.1

Rewrite $64$ as $8^{2}$ .

$4 {\sqrt{8^{2}}}^{3} y^{8} \cdot (4 \sqrt{121 h})$

Step 1.2

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

$4 \cdot 8^{3} y^{8} \cdot (4 \sqrt{121 h})$

Step 1.3

Raise $8$ to the power of $3$ .

$4 \cdot 512 y^{8} \cdot (4 \sqrt{121 h})$

Step 1.4

Multiply $4$ by $512$ .

$2048 y^{8} \cdot (4 \sqrt{121 h})$

Step 1.5

Rewrite $121$ as $11^{2}$ .

$2048 y^{8} \cdot (4 \sqrt{11^{2} h})$

Step 2

Pull terms out from under the radical.

$2048 y^{8} \cdot (4 (11 \sqrt{h}))$

Step 3

Multiply.

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Step 3.1

Multiply $11$ by $4$ .

$2048 y^{8} \cdot (44 \sqrt{h})$

Step 3.2

Multiply $44$ by $2048$ .

$90112 y^{8} \sqrt{h}$