Solve (2^-1div5^-1)^2*(-5/8)^-1

$$( 2 ^ { - 1 } \div 5 ^ { - 1 } ) ^ { 2 } \times ( \frac { - 5 } { 8 } ) ^ { - 1 }$$

Evaluate

$$-10$$

Solution Steps

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

$$\left(\frac{\frac{1}{2}}{5^{-1}}\right)^{2}\times \left(\frac{-5}{8}\right)^{-1}$$

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

$$\left(\frac{\frac{1}{2}}{\frac{1}{5}}\right)^{2}\times \left(\frac{-5}{8}\right)^{-1}$$

Divide \frac{1}{2} by \frac{1}{5} by multiplying \frac{1}{2} by the reciprocal of \frac{1}{5}.

$$\left(\frac{1}{2}\times 5\right)^{2}\times \left(\frac{-5}{8}\right)^{-1}$$

Multiply \frac{1}{2} and 5 to get \frac{5}{2}.

$$\left(\frac{5}{2}\right)^{2}\times \left(\frac{-5}{8}\right)^{-1}$$

Calculate \frac{5}{2} to the power of 2 and get \frac{25}{4}.

$$\frac{25}{4}\times \left(\frac{-5}{8}\right)^{-1}$$

Fraction \frac{-5}{8} can be rewritten as -\frac{5}{8} by extracting the negative sign.

$$\frac{25}{4}\left(-\frac{5}{8}\right)^{-1}$$

Calculate -\frac{5}{8} to the power of -1 and get -\frac{8}{5}.

$$\frac{25}{4}\left(-\frac{8}{5}\right)$$

Multiply \frac{25}{4} and -\frac{8}{5} to get -10.

$$-10$$

Factor

$$-10$$