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

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

Evaluate

$$-\frac{1}{1024}=-0.000976562$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 2 and 5 to get 7.

$$\left(\frac{1}{2}\right)^{7}\left(-\frac{1}{2}\right)^{3}$$

Calculate \frac{1}{2} to the power of 7 and get \frac{1}{128}.

$$\frac{1}{128}\left(-\frac{1}{2}\right)^{3}$$

Calculate -\frac{1}{2} to the power of 3 and get -\frac{1}{8}.

$$\frac{1}{128}\left(-\frac{1}{8}\right)$$

Multiply \frac{1}{128} times -\frac{1}{8} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1\left(-1\right)}{128\times 8}$$

Do the multiplications in the fraction \frac{1\left(-1\right)}{128\times 8}.

$$\frac{-1}{1024}$$

Fraction \frac{-1}{1024} can be rewritten as -\frac{1}{1024} by extracting the negative sign.

$$-\frac{1}{1024}$$

Factor

$$-\frac{1}{1024} = -0.0009765625$$