Solve -3|1-5|+2(3-5)^2/(4-8)^2+2(-1)^15

$$\frac { - 3 | 1 - 5 | + 2 ( 3 - 5 ) ^ { 2 } } { ( 4 - 8 ) ^ { 2 } + 2 ( - 1 ) ^ { 15 } }$$

Evaluate

$$-\frac{2}{7}\approx -0.285714286$$

Solution Steps

Subtract 5 from 1 to get -4.

$$\frac{-3|-4|+2\left(3-5\right)^{2}}{\left(4-8\right)^{2}+2\left(-1\right)^{15}}$$

The absolute value of a real number a is a when a\geq 0, or -a when a<0. The absolute value of -4 is 4.

$$\frac{-3\times 4+2\left(3-5\right)^{2}}{\left(4-8\right)^{2}+2\left(-1\right)^{15}}$$

Multiply -3 and 4 to get -12.

$$\frac{-12+2\left(3-5\right)^{2}}{\left(4-8\right)^{2}+2\left(-1\right)^{15}}$$

Subtract 5 from 3 to get -2.

$$\frac{-12+2\left(-2\right)^{2}}{\left(4-8\right)^{2}+2\left(-1\right)^{15}}$$

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

$$\frac{-12+2\times 4}{\left(4-8\right)^{2}+2\left(-1\right)^{15}}$$

Multiply 2 and 4 to get 8.

$$\frac{-12+8}{\left(4-8\right)^{2}+2\left(-1\right)^{15}}$$

Add -12 and 8 to get -4.

$$\frac{-4}{\left(4-8\right)^{2}+2\left(-1\right)^{15}}$$

Subtract 8 from 4 to get -4.

$$\frac{-4}{\left(-4\right)^{2}+2\left(-1\right)^{15}}$$

Calculate -4 to the power of 2 and get 16.

$$\frac{-4}{16+2\left(-1\right)^{15}}$$

Calculate -1 to the power of 15 and get -1.

$$\frac{-4}{16+2\left(-1\right)}$$

Multiply 2 and -1 to get -2.

$$\frac{-4}{16-2}$$

Subtract 2 from 16 to get 14.

$$\frac{-4}{14}$$

Reduce the fraction \frac{-4}{14} to lowest terms by extracting and canceling out 2.

$$-\frac{2}{7}$$

Factor

$$-\frac{2}{7} = -0.2857142857142857$$