Solve sqrt{1/16}+1/41/2-{left(2/8right)}^-2

$$\sqrt{ \frac{ 1 }{ 16 } } + \frac{ 1 }{ 4 } \frac{ 1 }{ 2 } - { \left( \frac{ 2 }{ 8 } \right) }^{ -2 }$$

Evaluate

$$-\frac{125}{8}=-15.625$$

Solution Steps

Rewrite the square root of the division \frac{1}{16} as the division of square roots \frac{\sqrt{1}}{\sqrt{16}}. Take the square root of both numerator and denominator.

$$\frac{1}{4}+\frac{1}{4}\times \frac{1}{2}-\left(\frac{2}{8}\right)^{-2}$$

Multiply \frac{1}{4} and \frac{1}{2} to get \frac{1}{8}.

$$\frac{1}{4}+\frac{1}{8}-\left(\frac{2}{8}\right)^{-2}$$

Add \frac{1}{4} and \frac{1}{8} to get \frac{3}{8}.

$$\frac{3}{8}-\left(\frac{2}{8}\right)^{-2}$$

Reduce the fraction \frac{2}{8} to lowest terms by extracting and canceling out 2.

$$\frac{3}{8}-\left(\frac{1}{4}\right)^{-2}$$

Calculate \frac{1}{4} to the power of -2 and get 16.

$$\frac{3}{8}-16$$

Subtract 16 from \frac{3}{8} to get -\frac{125}{8}.

$$-\frac{125}{8}$$

Factor

$$-\frac{125}{8} = -15\frac{5}{8} = -15.625$$