Algebra Examples

$\sqrt[5]{- 16} \cdot 2^{\frac{1}{5}}$

Step 1

Rewrite $- 16$ as ${(- 1)}^{5} \cdot 16$ .

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Step 1.1

Rewrite $- 16$ as $- 1 (16)$ .

$\sqrt[5]{- 1 (16)} \cdot 2^{\frac{1}{5}}$

Step 1.2

Rewrite $- 1$ as ${(- 1)}^{5}$ .

$\sqrt[5]{{(- 1)}^{5} \cdot 16} \cdot 2^{\frac{1}{5}}$

Step 2

Pull terms out from under the radical.

$- 1 \sqrt[5]{16} \cdot 2^{\frac{1}{5}}$

Step 3

Rewrite $- 1 \sqrt[5]{16}$ as $- \sqrt[5]{16}$ .

$- \sqrt[5]{16} \cdot 2^{\frac{1}{5}}$

Step 4

Multiply $- \sqrt[5]{16} \cdot 2^{\frac{1}{5}}$ .

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Step 4.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[5]{16}$ as $16^{\frac{1}{5}}$ .

$- (2^{\frac{1}{5}} \cdot 16^{\frac{1}{5}})$

Step 4.2

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

$- (2^{\frac{1}{5}} \cdot {(2^{4})}^{\frac{1}{5}})$

Step 4.3

Multiply the exponents in ${(2^{4})}^{\frac{1}{5}}$ .

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Step 4.3.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$- (2^{\frac{1}{5}} \cdot 2^{4 (\frac{1}{5})})$

Step 4.3.2

Combine $4$ and $\frac{1}{5}$ .

$- (2^{\frac{1}{5}} \cdot 2^{\frac{4}{5}})$

Step 4.4

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

$- 2^{\frac{1}{5} + \frac{4}{5}}$

Step 4.5

Combine the numerators over the common denominator.

$- 2^{\frac{1 + 4}{5}}$

Step 4.6

Add $1$ and $4$ .

$- 2^{\frac{5}{5}}$

Step 4.7

Cancel the common factor of $5$ .

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Step 4.7.1

Cancel the common factor.

$- 2^{\frac{5}{5}}$

Step 4.7.2

Rewrite the expression.

$- 2^{1}$

Step 5

Evaluate the exponent.

$- 1 \cdot 2$

Step 6

Multiply $- 1$ by $2$ .

$- 2$