Solve [(-1/2)^4:(-1/2)^3]*(-1/2)^6-2^-7

$$[ ( - 1 / 2 ) ^ { 4 } : ( - 1 / 2 ) ^ { 3 } ] \cdot ( - 1 / 2 ) ^ { 6 } - 2 ^ { - 7 }$$

Evaluate

$$-\frac{1}{64}=-0.015625$$

Solution Steps

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 3 from 4 to get 1.

$$\left(-\frac{1}{2}\right)^{1}\left(-\frac{1}{2}\right)^{6}-2^{-7}$$

To multiply powers of the same base, add their exponents. Add 1 and 6 to get 7.

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

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

$$-\frac{1}{128}-2^{-7}$$

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

$$-\frac{1}{128}-\frac{1}{128}$$

Subtract \frac{1}{128} from -\frac{1}{128} to get -\frac{1}{64}.

$$-\frac{1}{64}$$

Factor

$$-\frac{1}{64} = -0.015625$$