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

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

Evaluate

$$-\frac{3}{8}=-0.375$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

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

Calculate -3 to the power of 3 and get -27.

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

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

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

Multiply -27 and \frac{1}{32} to get \frac{-27}{32}.

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

Fraction \frac{-27}{32} can be rewritten as -\frac{27}{32} by extracting the negative sign.

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

Calculate -\frac{3}{2} to the power of 2 and get \frac{9}{4}.

$$\frac{-\frac{27}{32}}{\frac{9}{4}}$$

Divide -\frac{27}{32} by \frac{9}{4} by multiplying -\frac{27}{32} by the reciprocal of \frac{9}{4}.

$$-\frac{27}{32}\times \frac{4}{9}$$

Multiply -\frac{27}{32} times \frac{4}{9} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-27\times 4}{32\times 9}$$

Do the multiplications in the fraction \frac{-27\times 4}{32\times 9}.

$$\frac{-108}{288}$$

Reduce the fraction \frac{-108}{288} to lowest terms by extracting and canceling out 36.

$$-\frac{3}{8}$$

Factor

$$-\frac{3}{8} = -0.375$$