Algebra Examples

$\frac{72 \div (\sqrt{100} - 4^{2})}{\sqrt[3]{27}}$

Step 1

Multiply the numerator by the reciprocal of the denominator.

$72 \div (\sqrt{100} - 4^{2}) \cdot \frac{1}{\sqrt[3]{27}}$

Step 2

Rewrite the division as a fraction.

$\frac{72}{\sqrt{100} - 4^{2}} \cdot \frac{1}{\sqrt[3]{27}}$

Step 3

Simplify the denominator.

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Step 3.1

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

$\frac{72}{\sqrt{10^{2}} - 4^{2}} \cdot \frac{1}{\sqrt[3]{27}}$

Step 3.2

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

$\frac{72}{10 - 4^{2}} \cdot \frac{1}{\sqrt[3]{27}}$

Step 3.3

Raise $4$ to the power of $2$ .

$\frac{72}{10 - 1 \cdot 16} \cdot \frac{1}{\sqrt[3]{27}}$

Step 3.4

Multiply $- 1$ by $16$ .

$\frac{72}{10 - 16} \cdot \frac{1}{\sqrt[3]{27}}$

Step 3.5

Subtract $16$ from $10$ .

$\frac{72}{- 6} \cdot \frac{1}{\sqrt[3]{27}}$

Step 4

Divide $72$ by $- 6$ .

$- 12 \frac{1}{\sqrt[3]{27}}$

Step 5

Simplify the denominator.

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Step 5.1

Rewrite $27$ as $3^{3}$ .

$- 12 \frac{1}{\sqrt[3]{3^{3}}}$

Step 5.2

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

$- 12 (\frac{1}{3})$

Step 6

Cancel the common factor of $3$ .

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Step 6.1

Factor $3$ out of $- 12$ .

$3 (- 4) \frac{1}{3}$

Step 6.2

Cancel the common factor.

$3 \cdot - 4 \frac{1}{3}$

Step 6.3

Rewrite the expression.

$- 4$