Solve 2{left|2^5left|-left|-3^3right|-3right|1/2right|}^-2

$$2 { \left| { 2 }^{ 5 } \left| - \left| - { 3 }^{ 3 } \right| -3 \right| \frac{ 1 }{ 2 } \right| }^{ -2 }$$

Evaluate

$$\frac{8}{49}\approx 0.163265306$$

Solution Steps

Calculate 2 to the power of 5 and get 32.

$$2\left(|32|-|-3^{3}|-3|\frac{1}{2}|\right)^{-2}$$

The absolute value of a real number a is a when a\geq 0, or -a when a<0. The absolute value of 32 is 32.

$$2\left(32-|-3^{3}|-3|\frac{1}{2}|\right)^{-2}$$

Calculate 3 to the power of 3 and get 27.

$$2\left(32-|-27|-3|\frac{1}{2}|\right)^{-2}$$

The absolute value of a real number a is a when a\geq 0, or -a when a<0. The absolute value of -27 is 27.

$$2\left(32-27-3|\frac{1}{2}|\right)^{-2}$$

Subtract 27 from 32 to get 5.

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

The absolute value of a real number a is a when a\geq 0, or -a when a<0. The absolute value of \frac{1}{2} is \frac{1}{2}.

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

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

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

Subtract \frac{3}{2} from 5 to get \frac{7}{2}.

$$2\times \left(\frac{7}{2}\right)^{-2}$$

Calculate \frac{7}{2} to the power of -2 and get \frac{4}{49}.

$$2\times \frac{4}{49}$$

Multiply 2 and \frac{4}{49} to get \frac{8}{49}.

$$\frac{8}{49}$$

Factor

$$\frac{2 ^ {3}}{7 ^ {2}} = 0.16326530612244897$$