Solve 3/8ab^{2}div(-3/2a^2b)^3*(1/2a^2b)^2=

$$\frac { 3 } { 8 } a b ^ { 2 } \div ( - \frac { 3 } { 2 } a ^ { 2 } b ) ^ { 3 } \times ( \frac { 1 } { 2 } a ^ { 2 } b ) ^ { 2 } =$$

Evaluate

$$-\frac{b}{36a}$$

Solution Steps

Expand \left(-\frac{3}{2}a^{2}b\right)^{3}.

$$\frac{\frac{3}{8}ab^{2}}{\left(-\frac{3}{2}\right)^{3}\left(a^{2}\right)^{3}b^{3}}\times \left(\frac{1}{2}a^{2}b\right)^{2}$$

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

$$\frac{\frac{3}{8}ab^{2}}{\left(-\frac{3}{2}\right)^{3}a^{6}b^{3}}\times \left(\frac{1}{2}a^{2}b\right)^{2}$$

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

$$\frac{\frac{3}{8}ab^{2}}{-\frac{27}{8}a^{6}b^{3}}\times \left(\frac{1}{2}a^{2}b\right)^{2}$$

Cancel out ab^{2} in both numerator and denominator.

$$\frac{\frac{3}{8}}{-\frac{27}{8}ba^{5}}\times \left(\frac{1}{2}a^{2}b\right)^{2}$$

Express \frac{\frac{3}{8}}{-\frac{27}{8}ba^{5}} as a single fraction.

$$\frac{3}{8\left(-\frac{27}{8}\right)ba^{5}}\times \left(\frac{1}{2}a^{2}b\right)^{2}$$

Multiply 8 and -\frac{27}{8} to get -27.

$$\frac{3}{-27ba^{5}}\times \left(\frac{1}{2}a^{2}b\right)^{2}$$

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

$$\frac{3}{-27ba^{5}}\times \left(\frac{1}{2}\right)^{2}\left(a^{2}\right)^{2}b^{2}$$

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

$$\frac{3}{-27ba^{5}}\times \left(\frac{1}{2}\right)^{2}a^{4}b^{2}$$

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

$$\frac{3}{-27ba^{5}}\times \frac{1}{4}a^{4}b^{2}$$

Multiply \frac{3}{-27ba^{5}} times \frac{1}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{3}{-27ba^{5}\times 4}a^{4}b^{2}$$

Express \frac{3}{-27ba^{5}\times 4}a^{4} as a single fraction.

$$\frac{3a^{4}}{-27ba^{5}\times 4}b^{2}$$

Cancel out 3a^{4} in both numerator and denominator.

$$\frac{1}{-9\times 4ab}b^{2}$$

Express \frac{1}{-9\times 4ab}b^{2} as a single fraction.

$$\frac{b^{2}}{-9\times 4ab}$$

Cancel out b in both numerator and denominator.

$$\frac{b}{-9\times 4a}$$

Multiply -9 and 4 to get -36.

$$\frac{b}{-36a}$$

Expand

$$-\frac{b}{36a}$$

Solution Steps

Expand \left(-\frac{3}{2}a^{2}b\right)^{3}.

$$\frac{\frac{3}{8}ab^{2}}{\left(-\frac{3}{2}\right)^{3}\left(a^{2}\right)^{3}b^{3}}\times \left(\frac{1}{2}a^{2}b\right)^{2}$$

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

$$\frac{\frac{3}{8}ab^{2}}{\left(-\frac{3}{2}\right)^{3}a^{6}b^{3}}\times \left(\frac{1}{2}a^{2}b\right)^{2}$$

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

$$\frac{\frac{3}{8}ab^{2}}{-\frac{27}{8}a^{6}b^{3}}\times \left(\frac{1}{2}a^{2}b\right)^{2}$$

Cancel out ab^{2} in both numerator and denominator.

$$\frac{\frac{3}{8}}{-\frac{27}{8}ba^{5}}\times \left(\frac{1}{2}a^{2}b\right)^{2}$$

Express \frac{\frac{3}{8}}{-\frac{27}{8}ba^{5}} as a single fraction.

$$\frac{3}{8\left(-\frac{27}{8}\right)ba^{5}}\times \left(\frac{1}{2}a^{2}b\right)^{2}$$

Multiply 8 and -\frac{27}{8} to get -27.

$$\frac{3}{-27ba^{5}}\times \left(\frac{1}{2}a^{2}b\right)^{2}$$

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

$$\frac{3}{-27ba^{5}}\times \left(\frac{1}{2}\right)^{2}\left(a^{2}\right)^{2}b^{2}$$

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

$$\frac{3}{-27ba^{5}}\times \left(\frac{1}{2}\right)^{2}a^{4}b^{2}$$

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

$$\frac{3}{-27ba^{5}}\times \frac{1}{4}a^{4}b^{2}$$

Multiply \frac{3}{-27ba^{5}} times \frac{1}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{3}{-27ba^{5}\times 4}a^{4}b^{2}$$

Express \frac{3}{-27ba^{5}\times 4}a^{4} as a single fraction.

$$\frac{3a^{4}}{-27ba^{5}\times 4}b^{2}$$

Cancel out 3a^{4} in both numerator and denominator.

$$\frac{1}{-9\times 4ab}b^{2}$$

Express \frac{1}{-9\times 4ab}b^{2} as a single fraction.

$$\frac{b^{2}}{-9\times 4ab}$$

Cancel out b in both numerator and denominator.

$$\frac{b}{-9\times 4a}$$

Multiply -9 and 4 to get -36.

$$\frac{b}{-36a}$$