Solve (sqrt[3]{frac{1/216})^-1+3(2sqrt{9})^3-3sqrt{64}}{(-2)^0-(-1/2)+sqrt[4]{1/16}}

$$\frac { ( \sqrt[ 3 ] { \frac { 1 } { 216 } } ) ^ { - 1 } + 3 ( 2 \sqrt { 9 } ) ^ { 3 } - 3 \sqrt { 64 } } { ( - 2 ) ^ { 0 } - ( - \frac { 1 } { 2 } ) + \sqrt[ 4 ] { \frac { 1 } { 16 } } }$$

Evaluate

$$315$$

Solution Steps

Calculate \sqrt[3]{\frac{1}{216}} and get \frac{1}{6}.

$$\frac{\left(\frac{1}{6}\right)^{-1}+3\times \left(2\sqrt{9}\right)^{3}-3\sqrt{64}}{\left(-2\right)^{0}-\left(-\frac{1}{2}\right)+\sqrt[4]{\frac{1}{16}}}$$

Calculate \frac{1}{6} to the power of -1 and get 6.

$$\frac{6+3\times \left(2\sqrt{9}\right)^{3}-3\sqrt{64}}{\left(-2\right)^{0}-\left(-\frac{1}{2}\right)+\sqrt[4]{\frac{1}{16}}}$$

Calculate the square root of 9 and get 3.

$$\frac{6+3\times \left(2\times 3\right)^{3}-3\sqrt{64}}{\left(-2\right)^{0}-\left(-\frac{1}{2}\right)+\sqrt[4]{\frac{1}{16}}}$$

Multiply 2 and 3 to get 6.

$$\frac{6+3\times 6^{3}-3\sqrt{64}}{\left(-2\right)^{0}-\left(-\frac{1}{2}\right)+\sqrt[4]{\frac{1}{16}}}$$

Calculate 6 to the power of 3 and get 216.

$$\frac{6+3\times 216-3\sqrt{64}}{\left(-2\right)^{0}-\left(-\frac{1}{2}\right)+\sqrt[4]{\frac{1}{16}}}$$

Multiply 3 and 216 to get 648.

$$\frac{6+648-3\sqrt{64}}{\left(-2\right)^{0}-\left(-\frac{1}{2}\right)+\sqrt[4]{\frac{1}{16}}}$$

Add 6 and 648 to get 654.

$$\frac{654-3\sqrt{64}}{\left(-2\right)^{0}-\left(-\frac{1}{2}\right)+\sqrt[4]{\frac{1}{16}}}$$

Calculate the square root of 64 and get 8.

$$\frac{654-3\times 8}{\left(-2\right)^{0}-\left(-\frac{1}{2}\right)+\sqrt[4]{\frac{1}{16}}}$$

Multiply -3 and 8 to get -24.

$$\frac{654-24}{\left(-2\right)^{0}-\left(-\frac{1}{2}\right)+\sqrt[4]{\frac{1}{16}}}$$

Subtract 24 from 654 to get 630.

$$\frac{630}{\left(-2\right)^{0}-\left(-\frac{1}{2}\right)+\sqrt[4]{\frac{1}{16}}}$$

Calculate -2 to the power of 0 and get 1.

$$\frac{630}{1-\left(-\frac{1}{2}\right)+\sqrt[4]{\frac{1}{16}}}$$

The opposite of -\frac{1}{2} is \frac{1}{2}.

$$\frac{630}{1+\frac{1}{2}+\sqrt[4]{\frac{1}{16}}}$$

Add 1 and \frac{1}{2} to get \frac{3}{2}.

$$\frac{630}{\frac{3}{2}+\sqrt[4]{\frac{1}{16}}}$$

Calculate \sqrt[4]{\frac{1}{16}} and get \frac{1}{2}.

$$\frac{630}{\frac{3}{2}+\frac{1}{2}}$$

Add \frac{3}{2} and \frac{1}{2} to get 2.

$$\frac{630}{2}$$

Divide 630 by 2 to get 315.

$$315$$

Factor

$$3^{2}\times 5\times 7$$