Solve (-a^2b)^3div(3/4ab)^2*9/2b^4

$$( - a ^ { 2 } b ) ^ { 3 } \div ( \frac { 3 } { 4 } a b ) ^ { 2 } \times \frac { 9 } { 2 } b ^ { 4 }$$

Evaluate

$$-8a^{4}b^{5}$$

Short Solution Steps

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

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

Expand \left(\frac{3}{4}ab\right)^{2}.

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

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

$$\frac{\left(-a^{2}\right)^{3}b^{3}}{\frac{9}{16}a^{2}b^{2}}\times \frac{9}{2}b^{4}$$

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

$$\frac{b\left(-a^{2}\right)^{3}}{\frac{9}{16}a^{2}}\times \frac{9}{2}b^{4}$$

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

$$\frac{b\left(-1\right)^{3}\left(a^{2}\right)^{3}}{\frac{9}{16}a^{2}}\times \frac{9}{2}b^{4}$$

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

$$\frac{b\left(-1\right)^{3}a^{6}}{\frac{9}{16}a^{2}}\times \frac{9}{2}b^{4}$$

Calculate -1 to the power of 3 and get -1.

$$\frac{b\left(-1\right)a^{6}}{\frac{9}{16}a^{2}}\times \frac{9}{2}b^{4}$$

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

$$\frac{-ba^{4}}{\frac{9}{16}}\times \frac{9}{2}b^{4}$$

Divide -ba^{4} by \frac{9}{16} by multiplying -ba^{4} by the reciprocal of \frac{9}{16}.

$$\frac{-ba^{4}\times 16}{9}\times \frac{9}{2}b^{4}$$

Multiply -1 and 16 to get -16.

$$\frac{-16ba^{4}}{9}\times \frac{9}{2}b^{4}$$

Multiply \frac{-16ba^{4}}{9} times \frac{9}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-16ba^{4}\times 9}{9\times 2}b^{4}$$

Cancel out 2\times 9 in both numerator and denominator.

$$-8ba^{4}b^{4}$$

To multiply powers of the same base, add their exponents. Add 1 and 4 to get 5.

$$-8b^{5}a^{4}$$

Expand

$$-8a^{4}b^{5}$$

Short Solution Steps

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

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

Expand \left(\frac{3}{4}ab\right)^{2}.

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

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

$$\frac{\left(-a^{2}\right)^{3}b^{3}}{\frac{9}{16}a^{2}b^{2}}\times \frac{9}{2}b^{4}$$

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

$$\frac{b\left(-a^{2}\right)^{3}}{\frac{9}{16}a^{2}}\times \frac{9}{2}b^{4}$$

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

$$\frac{b\left(-1\right)^{3}\left(a^{2}\right)^{3}}{\frac{9}{16}a^{2}}\times \frac{9}{2}b^{4}$$

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

$$\frac{b\left(-1\right)^{3}a^{6}}{\frac{9}{16}a^{2}}\times \frac{9}{2}b^{4}$$

Calculate -1 to the power of 3 and get -1.

$$\frac{b\left(-1\right)a^{6}}{\frac{9}{16}a^{2}}\times \frac{9}{2}b^{4}$$

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

$$\frac{-ba^{4}}{\frac{9}{16}}\times \frac{9}{2}b^{4}$$

Divide -ba^{4} by \frac{9}{16} by multiplying -ba^{4} by the reciprocal of \frac{9}{16}.

$$\frac{-ba^{4}\times 16}{9}\times \frac{9}{2}b^{4}$$

Multiply -1 and 16 to get -16.

$$\frac{-16ba^{4}}{9}\times \frac{9}{2}b^{4}$$

Multiply \frac{-16ba^{4}}{9} times \frac{9}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-16ba^{4}\times 9}{9\times 2}b^{4}$$

Cancel out 2\times 9 in both numerator and denominator.

$$-8ba^{4}b^{4}$$

To multiply powers of the same base, add their exponents. Add 1 and 4 to get 5.

$$-8b^{5}a^{4}$$