Algebra Examples

$\sqrt[5]{{(- 2)}^{10} (3^{5}) (2^{3})}$

Step 1

Rewrite $- 2$ as $- 1 (2)$ .

$\sqrt[5]{{(- 1 (2))}^{10} \cdot 3^{5} \cdot 2^{3}}$

Step 2

Simplify the expression.

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Step 2.1

Apply the product rule to $- 1 (2)$ .

$\sqrt[5]{{(- 1)}^{10} \cdot 2^{10} \cdot 3^{5} \cdot 2^{3}}$

Step 2.2

Raise $- 1$ to the power of $10$ .

$\sqrt[5]{1 \cdot 2^{10} \cdot 3^{5} \cdot 2^{3}}$

Step 2.3

Multiply $2^{10}$ by $1$ .

$\sqrt[5]{2^{10} \cdot 3^{5} \cdot 2^{3}}$

Step 3

Multiply $2^{10}$ by $2^{3}$ by adding the exponents.

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Step 3.1

Move $2^{3}$ .

$\sqrt[5]{2^{3} \cdot 2^{10} \cdot 3^{5}}$

Step 3.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\sqrt[5]{2^{3 + 10} \cdot 3^{5}}$

Step 3.3

Add $3$ and $10$ .

$\sqrt[5]{2^{13} \cdot 3^{5}}$

Step 4

Raise $2$ to the power of $13$ .

$\sqrt[5]{8192 \cdot 3^{5}}$

Step 5

Raise $3$ to the power of $5$ .

$\sqrt[5]{8192 \cdot 243}$

Step 6

Multiply $8192$ by $243$ .

$\sqrt[5]{1990656}$

Step 7

Rewrite $1990656$ as $12^{5} \cdot 8$ .

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Step 7.1

Factor $248832$ out of $1990656$ .

$\sqrt[5]{248832 (8)}$

Step 7.2

Rewrite $248832$ as $12^{5}$ .

$\sqrt[5]{12^{5} \cdot 8}$

Step 8

Pull terms out from under the radical.

$12 \sqrt[5]{8}$

Step 9

The result can be shown in multiple forms.

Exact Form:

$12 \sqrt[5]{8}$

Decimal Form:

$18.18859879 \dots$