Solve [(-7/4ab^2c):(-7/2ac)]^2:(+3/2b^3)

$$[ ( - \frac { 7 } { 4 } a b ^ { 2 } c ) : ( - \frac { 7 } { 2 } a c ) ] ^ { 2 } : ( + \frac { 3 } { 2 } b ^ { 3 } )$$

Evaluate

$$\frac{b}{6}$$

Solution Steps

Cancel out ac in both numerator and denominator.

$$\frac{\left(\frac{-\frac{7}{4}b^{2}}{-\frac{7}{2}}\right)^{2}}{\frac{3}{2}b^{3}}$$

Divide -\frac{7}{4}b^{2} by -\frac{7}{2} by multiplying -\frac{7}{4}b^{2} by the reciprocal of -\frac{7}{2}.

$$\frac{\left(\frac{-\frac{7}{4}b^{2}\times 2}{-7}\right)^{2}}{\frac{3}{2}b^{3}}$$

Multiply -\frac{7}{4} and 2 to get -\frac{7}{2}.

$$\frac{\left(\frac{-\frac{7}{2}b^{2}}{-7}\right)^{2}}{\frac{3}{2}b^{3}}$$

Divide -\frac{7}{2}b^{2} by -7 to get \frac{1}{2}b^{2}.

$$\frac{\left(\frac{1}{2}b^{2}\right)^{2}}{\frac{3}{2}b^{3}}$$

Expand \left(\frac{1}{2}b^{2}\right)^{2}.

$$\frac{\left(\frac{1}{2}\right)^{2}\left(b^{2}\right)^{2}}{\frac{3}{2}b^{3}}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

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

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

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

Cancel out b^{3} in both numerator and denominator.

$$\frac{\frac{1}{4}b}{\frac{3}{2}}$$

Divide \frac{1}{4}b by \frac{3}{2} by multiplying \frac{1}{4}b by the reciprocal of \frac{3}{2}.

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

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

$$\frac{\frac{1}{2}b}{3}$$

Divide \frac{1}{2}b by 3 to get \frac{1}{6}b.

$$\frac{1}{6}b$$

Expand

$$\frac{b}{6}$$

Solution Steps

Cancel out ac in both numerator and denominator.

$$\frac{\left(\frac{-\frac{7}{4}b^{2}}{-\frac{7}{2}}\right)^{2}}{\frac{3}{2}b^{3}}$$

Divide -\frac{7}{4}b^{2} by -\frac{7}{2} by multiplying -\frac{7}{4}b^{2} by the reciprocal of -\frac{7}{2}.

$$\frac{\left(\frac{-\frac{7}{4}b^{2}\times 2}{-7}\right)^{2}}{\frac{3}{2}b^{3}}$$

Multiply -\frac{7}{4} and 2 to get -\frac{7}{2}.

$$\frac{\left(\frac{-\frac{7}{2}b^{2}}{-7}\right)^{2}}{\frac{3}{2}b^{3}}$$

Divide -\frac{7}{2}b^{2} by -7 to get \frac{1}{2}b^{2}.

$$\frac{\left(\frac{1}{2}b^{2}\right)^{2}}{\frac{3}{2}b^{3}}$$

Expand \left(\frac{1}{2}b^{2}\right)^{2}.

$$\frac{\left(\frac{1}{2}\right)^{2}\left(b^{2}\right)^{2}}{\frac{3}{2}b^{3}}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

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

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

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

Cancel out b^{3} in both numerator and denominator.

$$\frac{\frac{1}{4}b}{\frac{3}{2}}$$

Divide \frac{1}{4}b by \frac{3}{2} by multiplying \frac{1}{4}b by the reciprocal of \frac{3}{2}.

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

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

$$\frac{\frac{1}{2}b}{3}$$

Divide \frac{1}{2}b by 3 to get \frac{1}{6}b.

$$\frac{1}{6}b$$