Solve 2^3+2^2[2(sqrt{49}-sqrt{36})(1-sqrt{9})-sqrt[3]{8/64}]

$$2 ^ { 3 } + 2 ^ { 2 } [ 2 ( \sqrt { 49 } - \sqrt { 36 } ) ( 1 - \sqrt { 9 } ) - \sqrt[ 3 ] { \frac { 8 } { 64 } } ]$$

Evaluate

$$-10$$

Solution Steps

Calculate 2 to the power of 3 and get 8.

$$8+2^{2}\left(2\left(\sqrt{49}-\sqrt{36}\right)\left(1-\sqrt{9}\right)-\sqrt[3]{\frac{8}{64}}\right)$$

Calculate 2 to the power of 2 and get 4.

$$8+4\left(2\left(\sqrt{49}-\sqrt{36}\right)\left(1-\sqrt{9}\right)-\sqrt[3]{\frac{8}{64}}\right)$$

Calculate the square root of 49 and get 7.

$$8+4\left(2\left(7-\sqrt{36}\right)\left(1-\sqrt{9}\right)-\sqrt[3]{\frac{8}{64}}\right)$$

Calculate the square root of 36 and get 6.

$$8+4\left(2\left(7-6\right)\left(1-\sqrt{9}\right)-\sqrt[3]{\frac{8}{64}}\right)$$

Subtract 6 from 7 to get 1.

$$8+4\left(2\times 1\left(1-\sqrt{9}\right)-\sqrt[3]{\frac{8}{64}}\right)$$

Multiply 2 and 1 to get 2.

$$8+4\left(2\left(1-\sqrt{9}\right)-\sqrt[3]{\frac{8}{64}}\right)$$

Calculate the square root of 9 and get 3.

$$8+4\left(2\left(1-3\right)-\sqrt[3]{\frac{8}{64}}\right)$$

Subtract 3 from 1 to get -2.

$$8+4\left(2\left(-2\right)-\sqrt[3]{\frac{8}{64}}\right)$$

Multiply 2 and -2 to get -4.

$$8+4\left(-4-\sqrt[3]{\frac{8}{64}}\right)$$

Reduce the fraction \frac{8}{64} to lowest terms by extracting and canceling out 8.

$$8+4\left(-4-\sqrt[3]{\frac{1}{8}}\right)$$

Calculate \sqrt[3]{\frac{1}{8}} and get \frac{1}{2}.

$$8+4\left(-4-\frac{1}{2}\right)$$

Subtract \frac{1}{2} from -4 to get -\frac{9}{2}.

$$8+4\left(-\frac{9}{2}\right)$$

Multiply 4 and -\frac{9}{2} to get -18.

$$8-18$$

Subtract 18 from 8 to get -10.

$$-10$$

Factor

$$-10$$