Simplify (10+7)-40/( cube root of 1000)

$(10 + 7) - \frac{40}{\sqrt[3]{1000}}$

Step 1

Find the common denominator.

Write $10$ as a fraction with denominator $1$ .

$\frac{10}{1} + 7 - \frac{40}{\sqrt[3]{1000}}$

Multiply $\frac{10}{1}$ by $\frac{\sqrt[3]{1000}}{\sqrt[3]{1000}}$ .

$\frac{10}{1} \cdot \frac{\sqrt[3]{1000}}{\sqrt[3]{1000}} + 7 - \frac{40}{\sqrt[3]{1000}}$

Multiply $\frac{10}{1}$ by $\frac{\sqrt[3]{1000}}{\sqrt[3]{1000}}$ .

$\frac{10 \sqrt[3]{1000}}{\sqrt[3]{1000}} + 7 - \frac{40}{\sqrt[3]{1000}}$

Write $7$ as a fraction with denominator $1$ .

$\frac{10 \sqrt[3]{1000}}{\sqrt[3]{1000}} + \frac{7}{1} - \frac{40}{\sqrt[3]{1000}}$

Multiply $\frac{7}{1}$ by $\frac{\sqrt[3]{1000}}{\sqrt[3]{1000}}$ .

$\frac{10 \sqrt[3]{1000}}{\sqrt[3]{1000}} + \frac{7}{1} \cdot \frac{\sqrt[3]{1000}}{\sqrt[3]{1000}} - \frac{40}{\sqrt[3]{1000}}$

Multiply $\frac{7}{1}$ by $\frac{\sqrt[3]{1000}}{\sqrt[3]{1000}}$ .

$\frac{10 \sqrt[3]{1000}}{\sqrt[3]{1000}} + \frac{7 \sqrt[3]{1000}}{\sqrt[3]{1000}} - \frac{40}{\sqrt[3]{1000}}$

Step 2

Simplify terms.

Combine the numerators over the common denominator.

$\frac{10 \sqrt[3]{1000} + 7 \sqrt[3]{1000} - 40}{\sqrt[3]{1000}}$

Simplify each term.

Rewrite $1000$ as $10^{3}$ .

$\frac{10 \sqrt[3]{10^{3}} + 7 \sqrt[3]{1000} - 40}{\sqrt[3]{1000}}$

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

$\frac{10 \cdot 10 + 7 \sqrt[3]{1000} - 40}{\sqrt[3]{1000}}$

Multiply $10$ by $10$ .

$\frac{100 + 7 \sqrt[3]{1000} - 40}{\sqrt[3]{1000}}$

Rewrite $1000$ as $10^{3}$ .

$\frac{100 + 7 \sqrt[3]{10^{3}} - 40}{\sqrt[3]{1000}}$

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

$\frac{100 + 7 \cdot 10 - 40}{\sqrt[3]{1000}}$

Multiply $7$ by $10$ .

$\frac{100 + 70 - 40}{\sqrt[3]{1000}}$

Simplify by adding and subtracting.

Add $100$ and $70$ .

$\frac{170 - 40}{\sqrt[3]{1000}}$

Subtract $40$ from $170$ .

$\frac{130}{\sqrt[3]{1000}}$

Step 3

Simplify the denominator.

Rewrite $1000$ as $10^{3}$ .

$\frac{130}{\sqrt[3]{10^{3}}}$

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

$\frac{130}{10}$

Step 4

Divide $130$ by $10$ .

$13$