Solve (3/4)^2*(2/3)^3*(1/2)^2

$$( \frac { 3 } { 4 } ) ^ { 2 } \times ( \frac { 2 } { 3 } ) ^ { 3 } \times ( \frac { 1 } { 2 } ) ^ { 2 }$$

Evaluate

$$\frac{1}{24}\approx 0.041666667$$

Solution Steps

Calculate \frac{3}{4} to the power of 2 and get \frac{9}{16}.

$$\frac{9}{16}\times \left(\frac{2}{3}\right)^{3}\times \left(\frac{1}{2}\right)^{2}$$

Calculate \frac{2}{3} to the power of 3 and get \frac{8}{27}.

$$\frac{9}{16}\times \frac{8}{27}\times \left(\frac{1}{2}\right)^{2}$$

Multiply \frac{9}{16} times \frac{8}{27} by multiplying numerator times numerator and denominator times denominator.

$$\frac{9\times 8}{16\times 27}\times \left(\frac{1}{2}\right)^{2}$$

Do the multiplications in the fraction \frac{9\times 8}{16\times 27}.

$$\frac{72}{432}\times \left(\frac{1}{2}\right)^{2}$$

Reduce the fraction \frac{72}{432} to lowest terms by extracting and canceling out 72.

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

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

$$\frac{1}{6}\times \frac{1}{4}$$

Multiply \frac{1}{6} times \frac{1}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1\times 1}{6\times 4}$$

Do the multiplications in the fraction \frac{1\times 1}{6\times 4}.

$$\frac{1}{24}$$

Factor

$$\frac{1}{2 ^ {3} \cdot 3} = 0.041666666666666664$$