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

$$- ( 6 : \frac { 2 } { 3 } ) ( \frac { 4 } { 3 } \cdot \frac { 1 } { 2 } ) ^ { 2 } ( \frac { 1 } { 2 } ) ^ { 2 }$$

Evaluate

$$-1$$

Solution Steps

Divide 6 by \frac{2}{3} by multiplying 6 by the reciprocal of \frac{2}{3}.

$$\left(-6\times \frac{3}{2}\right)\times \left(\frac{4}{3}\times \frac{1}{2}\right)^{2}\times \left(\frac{1}{2}\right)^{2}$$

Multiply 6 and \frac{3}{2} to get 9.

$$-9\times \left(\frac{4}{3}\times \frac{1}{2}\right)^{2}\times \left(\frac{1}{2}\right)^{2}$$

Multiply \frac{4}{3} and \frac{1}{2} to get \frac{2}{3}.

$$-9\times \left(\frac{2}{3}\right)^{2}\times \left(\frac{1}{2}\right)^{2}$$

Calculate \frac{2}{3} to the power of 2 and get \frac{4}{9}.

$$-9\times \frac{4}{9}\times \left(\frac{1}{2}\right)^{2}$$

Multiply -9 and \frac{4}{9} to get -4.

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

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

$$-4\times \frac{1}{4}$$

Multiply -4 and \frac{1}{4} to get -1.

$$-1$$

Factor

$$-1$$