Solve sqrt[3]{(4^3-2^2):(-10)-2}+(-3)^0(+3)^2-sqrt[3]{125}:sqrt[4]{+1}=

$$\sqrt[ 3 ] { ( 4 ^ { 3 } - 2 ^ { 2 } ) : ( - 10 ) - 2 } + ( - 3 ) ^ { 0 } ( + 3 ) ^ { 2 } - \sqrt[ 3 ] { 125 } : \sqrt[ 4 ] { + 1 } =$$

Evaluate

$$2$$

Solution Steps

Calculate 4 to the power of 3 and get 64.

$$\sqrt[3]{\frac{64-2^{2}}{-10}-2}+\left(-3\right)^{0}\times 3^{2}-\frac{\sqrt[3]{125}}{\sqrt[4]{1}}$$

Calculate 2 to the power of 2 and get 4.

$$\sqrt[3]{\frac{64-4}{-10}-2}+\left(-3\right)^{0}\times 3^{2}-\frac{\sqrt[3]{125}}{\sqrt[4]{1}}$$

Subtract 4 from 64 to get 60.

$$\sqrt[3]{\frac{60}{-10}-2}+\left(-3\right)^{0}\times 3^{2}-\frac{\sqrt[3]{125}}{\sqrt[4]{1}}$$

Divide 60 by -10 to get -6.

$$\sqrt[3]{-6-2}+\left(-3\right)^{0}\times 3^{2}-\frac{\sqrt[3]{125}}{\sqrt[4]{1}}$$

Subtract 2 from -6 to get -8.

$$\sqrt[3]{-8}+\left(-3\right)^{0}\times 3^{2}-\frac{\sqrt[3]{125}}{\sqrt[4]{1}}$$

Calculate \sqrt[3]{-8} and get -2.

$$-2+\left(-3\right)^{0}\times 3^{2}-\frac{\sqrt[3]{125}}{\sqrt[4]{1}}$$

Calculate -3 to the power of 0 and get 1.

$$-2+1\times 3^{2}-\frac{\sqrt[3]{125}}{\sqrt[4]{1}}$$

Calculate 3 to the power of 2 and get 9.

$$-2+1\times 9-\frac{\sqrt[3]{125}}{\sqrt[4]{1}}$$

Multiply 1 and 9 to get 9.

$$-2+9-\frac{\sqrt[3]{125}}{\sqrt[4]{1}}$$

Add -2 and 9 to get 7.

$$7-\frac{\sqrt[3]{125}}{\sqrt[4]{1}}$$

Calculate \sqrt[3]{125} and get 5.

$$7-\frac{5}{\sqrt[4]{1}}$$

Calculate \sqrt[4]{1} and get 1.

$$7-\frac{5}{1}$$

Anything divided by one gives itself.

$$7-5$$

Subtract 5 from 7 to get 2.

$$2$$

Factor

$$2$$