Solve 4^3(-12+2^2)/(2*3)^2+(-5*2*3)+2

$$\frac { 4 ^ { 3 } ( - 12 + 2 ^ { 2 } ) } { ( 2 \times 3 ) ^ { 2 } + ( - 5 \times 2 \times 3 ) } + 2$$

Evaluate

$$-\frac{250}{3}\approx -83.333333333$$

Solution Steps

Calculate 4 to the power of 3 and get 64.

$$\frac{64\left(-12+2^{2}\right)}{\left(2\times 3\right)^{2}-5\times 2\times 3}+2$$

Calculate 2 to the power of 2 and get 4.

$$\frac{64\left(-12+4\right)}{\left(2\times 3\right)^{2}-5\times 2\times 3}+2$$

Add -12 and 4 to get -8.

$$\frac{64\left(-8\right)}{\left(2\times 3\right)^{2}-5\times 2\times 3}+2$$

Multiply 64 and -8 to get -512.

$$\frac{-512}{\left(2\times 3\right)^{2}-5\times 2\times 3}+2$$

Multiply 2 and 3 to get 6.

$$\frac{-512}{6^{2}-5\times 2\times 3}+2$$

Calculate 6 to the power of 2 and get 36.

$$\frac{-512}{36-5\times 2\times 3}+2$$

Multiply -5 and 2 to get -10.

$$\frac{-512}{36-10\times 3}+2$$

Multiply -10 and 3 to get -30.

$$\frac{-512}{36-30}+2$$

Subtract 30 from 36 to get 6.

$$\frac{-512}{6}+2$$

Reduce the fraction \frac{-512}{6} to lowest terms by extracting and canceling out 2.

$$-\frac{256}{3}+2$$

Add -\frac{256}{3} and 2 to get -\frac{250}{3}.

$$-\frac{250}{3}$$

Factor

$$-\frac{250}{3} = -83\frac{1}{3} = -83.33333333333333$$