Basic Math Examples

${(\sqrt[3]{- 1} \div \sqrt[3]{64} \cdot \sqrt{16})}^{5}$

Step 1

Simplify the numerator.

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Step 1.1

Rewrite $- 1$ as ${(- 1)}^{3}$ .

${(\sqrt[3]{{(- 1)}^{3}} \div \sqrt[3]{64} \cdot \sqrt{16})}^{5}$

Step 1.2

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

${(- 1 \div \sqrt[3]{64} \cdot \sqrt{16})}^{5}$

Step 2

Simplify the denominator.

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Step 2.1

Rewrite $64$ as $4^{3}$ .

${(- 1 \div \sqrt[3]{4^{3}} \cdot \sqrt{16})}^{5}$

Step 2.2

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

${(- 1 \div 4 \cdot \sqrt{16})}^{5}$

Step 3

Rewrite the division as a fraction.

${(\frac{- 1}{4} \cdot \sqrt{16})}^{5}$

Step 4

Move the negative in front of the fraction.

${(- \frac{1}{4} \cdot \sqrt{16})}^{5}$

Step 5

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

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

Step 6

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

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

Step 7

Cancel the common factor of $4$ .

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Step 7.1

Move the leading negative in $- \frac{1}{4}$ into the numerator.

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

Step 7.2

Cancel the common factor.

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

Step 7.3

Rewrite the expression.

${(- 1)}^{5}$

Step 8

Raise $- 1$ to the power of $5$ .

$- 1$