Pre-Algebra Examples

$\sqrt[4]{2^{2} \cdot 3^{4} \cdot 5^{6} \cdot 7^{8}}$

Step 1

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

$\sqrt[4]{4 \cdot 3^{4} \cdot 5^{6} \cdot 7^{8}}$

Step 2

Raise $3$ to the power of $4$ .

$\sqrt[4]{4 \cdot 81 \cdot 5^{6} \cdot 7^{8}}$

Step 3

Raise $5$ to the power of $6$ .

$\sqrt[4]{4 \cdot 81 \cdot 15625 \cdot 7^{8}}$

Step 4

Raise $7$ to the power of $8$ .

$\sqrt[4]{4 \cdot 81 \cdot 15625 \cdot 5764801}$

Step 5

Combine exponents.

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Step 5.1

Multiply $4$ by $81$ .

$\sqrt[4]{324 \cdot 15625 \cdot 5764801}$

Step 5.2

Multiply $324$ by $15625$ .

$\sqrt[4]{5062500 \cdot 5764801}$

Step 5.3

Multiply $5062500$ by $5764801$ .

$\sqrt[4]{29184305062500}$

Step 6

Rewrite $29184305062500$ as $735^{4} \cdot 100$ .

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Step 6.1

Factor $291843050625$ out of $29184305062500$ .

$\sqrt[4]{291843050625 (100)}$

Step 6.2

Rewrite $291843050625$ as $735^{4}$ .

$\sqrt[4]{735^{4} \cdot 100}$

Step 7

Pull terms out from under the radical.

$735 \sqrt[4]{100}$

Step 8

Rewrite $100$ as $10^{2}$ .

$735 \sqrt[4]{10^{2}}$

Step 9

Rewrite $\sqrt[4]{10^{2}}$ as $\sqrt{\sqrt{10^{2}}}$ .

$735 \sqrt{\sqrt{10^{2}}}$

Step 10

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

$735 \sqrt{10}$

Step 11

The result can be shown in multiple forms.

Exact Form:

$735 \sqrt{10}$

Decimal Form:

$2324.27408022 \dots$