Solve frac{sqrt{sqrt[3]{125}}:sqrt[3]{-1}+[-7+3(-2)^2]sqrt{100}+(-2)^4:(-2)^2}{-1}

$$\frac { \sqrt { \sqrt[ 3 ] { 125 } } : \sqrt[ 3 ] { - 1 } + [ - 7 + 3 ( - 2 ) ^ { 2 } ] \sqrt { 100 } + ( - 2 ) ^ { 4 } : ( - 2 ) ^ { 2 } } { - 1 }$$

Evaluate

$$\sqrt{5}-54\approx -51.763932023$$

Solution Steps

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 2 from 4 to get 2.

$$\frac{\frac{\sqrt{\sqrt[3]{125}}}{\sqrt[3]{-1}}+\left(-7+3\left(-2\right)^{2}\right)\sqrt{100}+\left(-2\right)^{2}}{-1}$$

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

$$\frac{\frac{\sqrt{5}}{\sqrt[3]{-1}}+\left(-7+3\left(-2\right)^{2}\right)\sqrt{100}+\left(-2\right)^{2}}{-1}$$

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

$$\frac{\frac{\sqrt{5}}{-1}+\left(-7+3\left(-2\right)^{2}\right)\sqrt{100}+\left(-2\right)^{2}}{-1}$$

Anything divided by -1 gives its opposite.

$$\frac{-\sqrt{5}+\left(-7+3\left(-2\right)^{2}\right)\sqrt{100}+\left(-2\right)^{2}}{-1}$$

Calculate -2 to the power of 2 and get 4.

$$\frac{-\sqrt{5}+\left(-7+3\times 4\right)\sqrt{100}+\left(-2\right)^{2}}{-1}$$

Multiply 3 and 4 to get 12.

$$\frac{-\sqrt{5}+\left(-7+12\right)\sqrt{100}+\left(-2\right)^{2}}{-1}$$

Add -7 and 12 to get 5.

$$\frac{-\sqrt{5}+5\sqrt{100}+\left(-2\right)^{2}}{-1}$$

Calculate the square root of 100 and get 10.

$$\frac{-\sqrt{5}+5\times 10+\left(-2\right)^{2}}{-1}$$

Multiply 5 and 10 to get 50.

$$\frac{-\sqrt{5}+50+\left(-2\right)^{2}}{-1}$$

Calculate -2 to the power of 2 and get 4.

$$\frac{-\sqrt{5}+50+4}{-1}$$

Add 50 and 4 to get 54.

$$\frac{-\sqrt{5}+54}{-1}$$

Anything divided by -1 gives its opposite. To find the opposite of -\sqrt{5}+54, find the opposite of each term.

$$-\left(-\sqrt{5}\right)-54$$

Multiply -1 and -1 to get 1.

$$\sqrt{5}-54$$