Solve frac{sqrt[3]{(-3)^3}-sqrt[3]{-125}}{sqrt{5^2}+sqrt[3]{-1}}

$$\frac { \sqrt[ 3 ] { ( - 3 ) ^ { 3 } } - \sqrt[ 3 ] { - 125 } } { \sqrt { 5 ^ { 2 } } + \sqrt[ 3 ] { - 1 } }$$

Evaluate

$$\frac{1}{2}=0.5$$

Solution Steps

Calculate -3 to the power of 3 and get -27.

$$\frac{\sqrt[3]{-27}-\sqrt[3]{-125}}{\sqrt{5^{2}}+\sqrt[3]{-1}}$$

Calculate \sqrt[3]{-27} and get -3.

$$\frac{-3-\sqrt[3]{-125}}{\sqrt{5^{2}}+\sqrt[3]{-1}}$$

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

$$\frac{-3-\left(-5\right)}{\sqrt{5^{2}}+\sqrt[3]{-1}}$$

The opposite of -5 is 5.

$$\frac{-3+5}{\sqrt{5^{2}}+\sqrt[3]{-1}}$$

Add -3 and 5 to get 2.

$$\frac{2}{\sqrt{5^{2}}+\sqrt[3]{-1}}$$

Calculate 5 to the power of 2 and get 25.

$$\frac{2}{\sqrt{25}+\sqrt[3]{-1}}$$

Calculate the square root of 25 and get 5.

$$\frac{2}{5+\sqrt[3]{-1}}$$

Calculate \sqrt[3]{-1} and get -1.

$$\frac{2}{5-1}$$

Subtract 1 from 5 to get 4.

$$\frac{2}{4}$$

Reduce the fraction \frac{2}{4} to lowest terms by extracting and canceling out 2.

$$\frac{1}{2}$$

Factor

$$\frac{1}{2} = 0.5$$