Basic Math Examples

$(\sqrt{64}) {(\sqrt[4]{128})}^{3}$

Step 1

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

$\sqrt{8^{2}} {(\sqrt[4]{128})}^{3}$

Step 2

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

$8 {(\sqrt[4]{128})}^{3}$

Step 3

Rewrite $128$ as $2^{4} \cdot 8$ .

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Step 3.1

Factor $16$ out of $128$ .

$8 {\sqrt[4]{16 (8)}}^{3}$

Step 3.2

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

$8 {\sqrt[4]{2^{4} \cdot 8}}^{3}$

Step 4

Pull terms out from under the radical.

$8 {(2 \sqrt[4]{8})}^{3}$

Step 5

Simplify the expression.

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Step 5.1

Apply the product rule to $2 \sqrt[4]{8}$ .

$8 (2^{3} {\sqrt[4]{8}}^{3})$

Step 5.2

Raise $2$ to the power of $3$ .

$8 (8 {\sqrt[4]{8}}^{3})$

Step 6

Rewrite ${\sqrt[4]{8}}^{3}$ as $\sqrt[4]{8^{3}}$ .

$8 (8 \sqrt[4]{8^{3}})$

Step 7

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

$8 (8 \sqrt[4]{512})$

Step 8

Rewrite $512$ as $4^{4} \cdot 2$ .

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Step 8.1

Factor $256$ out of $512$ .

$8 (8 \sqrt[4]{256 (2)})$

Step 8.2

Rewrite $256$ as $4^{4}$ .

$8 (8 \sqrt[4]{4^{4} \cdot 2})$

Step 9

Pull terms out from under the radical.

$8 (8 (4 \sqrt[4]{2}))$

Step 10

Multiply.

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Step 10.1

Multiply $4$ by $8$ .

$8 (32 \sqrt[4]{2})$

Step 10.2

Multiply $32$ by $8$ .

$256 \sqrt[4]{2}$

Step 11

The result can be shown in multiple forms.

Exact Form:

$256 \sqrt[4]{2}$

Decimal Form:

$304.43702144 \dots$