Solve -3^3:(-2)^2-(-1/2)^5*2^3=

$$- 3 ^ { 3 } : ( - 2 ) ^ { 2 } - ( - \frac { 1 } { 2 } ) ^ { 5 } \cdot 2 ^ { 3 } =$$

Evaluate

$$-\frac{13}{2}=-6.5$$

Solution Steps

Calculate 3 to the power of 3 and get 27.

$$\frac{-27}{\left(-2\right)^{2}}-\left(-\frac{1}{2}\right)^{5}\times 2^{3}$$

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

$$\frac{-27}{4}-\left(-\frac{1}{2}\right)^{5}\times 2^{3}$$

Fraction \frac{-27}{4} can be rewritten as -\frac{27}{4} by extracting the negative sign.

$$-\frac{27}{4}-\left(-\frac{1}{2}\right)^{5}\times 2^{3}$$

Calculate -\frac{1}{2} to the power of 5 and get -\frac{1}{32}.

$$-\frac{27}{4}-\left(-\frac{1}{32}\times 2^{3}\right)$$

Calculate 2 to the power of 3 and get 8.

$$-\frac{27}{4}-\left(-\frac{1}{32}\times 8\right)$$

Express -\frac{1}{32}\times 8 as a single fraction.

$$-\frac{27}{4}-\frac{-8}{32}$$

Reduce the fraction \frac{-8}{32} to lowest terms by extracting and canceling out 8.

$$-\frac{27}{4}-\left(-\frac{1}{4}\right)$$

The opposite of -\frac{1}{4} is \frac{1}{4}.

$$-\frac{27}{4}+\frac{1}{4}$$

Since -\frac{27}{4} and \frac{1}{4} have the same denominator, add them by adding their numerators.

$$\frac{-27+1}{4}$$

Add -27 and 1 to get -26.

$$\frac{-26}{4}$$

Reduce the fraction \frac{-26}{4} to lowest terms by extracting and canceling out 2.

$$-\frac{13}{2}$$

Factor

$$-\frac{13}{2} = -6\frac{1}{2} = -6.5$$