Solve =(3/4*(2/3)^2*2/6/frac{3^2{4}*frac{2^3}{2}*frac{2^3}{3}})

$$= ( \frac { \frac { 3 } { 4 } \cdot ( \frac { 2 } { 3 } ) ^ { 2 } \cdot \frac { 2 } { 6 } } { \frac { 3 ^ { 2 } } { 4 } \cdot \frac { 2 ^ { 3 } } { 2 } \cdot \frac { 2 ^ { 3 } } { 3 } } )$$

Evaluate

$$\frac{1}{216}\approx 0.00462963$$

Solution Steps

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 1 from 3 to get 2.

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

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

$$\frac{\frac{3}{4}\times \frac{4}{9}\times \frac{2}{6}}{\frac{3^{2}}{4}\times 2^{2}\times \frac{2^{3}}{3}}$$

Multiply \frac{3}{4} times \frac{4}{9} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{3\times 4}{4\times 9}\times \frac{2}{6}}{\frac{3^{2}}{4}\times 2^{2}\times \frac{2^{3}}{3}}$$

Cancel out 4 in both numerator and denominator.

$$\frac{\frac{3}{9}\times \frac{2}{6}}{\frac{3^{2}}{4}\times 2^{2}\times \frac{2^{3}}{3}}$$

Reduce the fraction \frac{3}{9} to lowest terms by extracting and canceling out 3.

$$\frac{\frac{1}{3}\times \frac{2}{6}}{\frac{3^{2}}{4}\times 2^{2}\times \frac{2^{3}}{3}}$$

Reduce the fraction \frac{2}{6} to lowest terms by extracting and canceling out 2.

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

Multiply \frac{1}{3} times \frac{1}{3} by multiplying numerator times numerator and denominator times denominator.

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

Do the multiplications in the fraction \frac{1\times 1}{3\times 3}.

$$\frac{\frac{1}{9}}{\frac{3^{2}}{4}\times 2^{2}\times \frac{2^{3}}{3}}$$

Calculate 3 to the power of 2 and get 9.

$$\frac{\frac{1}{9}}{\frac{9}{4}\times 2^{2}\times \frac{2^{3}}{3}}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{\frac{1}{9}}{\frac{9}{4}\times 4\times \frac{2^{3}}{3}}$$

Cancel out 4 and 4.

$$\frac{\frac{1}{9}}{9\times \frac{2^{3}}{3}}$$

Calculate 2 to the power of 3 and get 8.

$$\frac{\frac{1}{9}}{9\times \frac{8}{3}}$$

Express 9\times \frac{8}{3} as a single fraction.

$$\frac{\frac{1}{9}}{\frac{9\times 8}{3}}$$

Multiply 9 and 8 to get 72.

$$\frac{\frac{1}{9}}{\frac{72}{3}}$$

Divide 72 by 3 to get 24.

$$\frac{\frac{1}{9}}{24}$$

Express \frac{\frac{1}{9}}{24} as a single fraction.

$$\frac{1}{9\times 24}$$

Multiply 9 and 24 to get 216.

$$\frac{1}{216}$$

Factor

$$\frac{1}{2 ^ {3} \cdot 3 ^ {3}} = 0.004629629629629629$$