Solve (1/2)^2/(frac{78^-2)^3}

$$\frac { ( \frac { 1 } { 2 } ) ^ { 2 } } { ( \frac { 7 } { 8 } ^ { - 2 } ) ^ { 3 } }$$

Evaluate

$$\frac{117649}{1048576}\approx 0.11219883$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply -2 and 3 to get -6.

$$\frac{\left(\frac{1}{2}\right)^{2}}{\left(\frac{7}{8}\right)^{-6}}$$

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

$$\frac{\frac{1}{4}}{\left(\frac{7}{8}\right)^{-6}}$$

Calculate \frac{7}{8} to the power of -6 and get \frac{262144}{117649}.

$$\frac{\frac{1}{4}}{\frac{262144}{117649}}$$

Divide \frac{1}{4} by \frac{262144}{117649} by multiplying \frac{1}{4} by the reciprocal of \frac{262144}{117649}.

$$\frac{1}{4}\times \frac{117649}{262144}$$

Multiply \frac{1}{4} and \frac{117649}{262144} to get \frac{117649}{1048576}.

$$\frac{117649}{1048576}$$

Factor

$$\frac{7 ^ {6}}{2 ^ {20}} = 0.1121988296508789$$