Solve [(-3a^{4}b)(-a^{2}b):(-2a^3b)]^3:(-9/4a^2b^3)

$$[ ( - 3 a ^ { 4 } b ) ( - a ^ { 2 } b ) : ( - 2 a ^ { 3 } b ) ] ^ { 3 } : ( - \frac { 9 } { 4 } a ^ { 2 } b ^ { 3 } )$$

Evaluate

$$\frac{3a^{7}}{2}$$

Solution Steps

Multiply b and b to get b^{2}.

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

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

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

Multiply -3 and -1 to get 3.

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

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

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

To raise \frac{3a^{3}b}{-2} to a power, raise both numerator and denominator to the power and then divide.

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

Express \frac{\frac{\left(3a^{3}b\right)^{3}}{\left(-2\right)^{3}}}{-\frac{9}{4}a^{2}b^{3}} as a single fraction.

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

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

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

To raise a power to another power, multiply the exponents. Multiply 3 and 3 to get 9.

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

Calculate 3 to the power of 3 and get 27.

$$\frac{27a^{9}b^{3}}{\left(-2\right)^{3}\left(-\frac{9}{4}\right)a^{2}b^{3}}$$

Calculate -2 to the power of 3 and get -8.

$$\frac{27a^{9}b^{3}}{-8\left(-\frac{9}{4}\right)a^{2}b^{3}}$$

Multiply -8 and -\frac{9}{4} to get 18.

$$\frac{27a^{9}b^{3}}{18a^{2}b^{3}}$$

Cancel out 9a^{2}b^{3} in both numerator and denominator.

$$\frac{3a^{7}}{2}$$

Expand

$$\frac{3a^{7}}{2}$$

Solution Steps

Multiply b and b to get b^{2}.

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

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

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

Multiply -3 and -1 to get 3.

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

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

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

To raise \frac{3a^{3}b}{-2} to a power, raise both numerator and denominator to the power and then divide.

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

Express \frac{\frac{\left(3a^{3}b\right)^{3}}{\left(-2\right)^{3}}}{-\frac{9}{4}a^{2}b^{3}} as a single fraction.

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

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

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

To raise a power to another power, multiply the exponents. Multiply 3 and 3 to get 9.

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

Calculate 3 to the power of 3 and get 27.

$$\frac{27a^{9}b^{3}}{\left(-2\right)^{3}\left(-\frac{9}{4}\right)a^{2}b^{3}}$$

Calculate -2 to the power of 3 and get -8.

$$\frac{27a^{9}b^{3}}{-8\left(-\frac{9}{4}\right)a^{2}b^{3}}$$

Multiply -8 and -\frac{9}{4} to get 18.

$$\frac{27a^{9}b^{3}}{18a^{2}b^{3}}$$

Cancel out 9a^{2}b^{3} in both numerator and denominator.

$$\frac{3a^{7}}{2}$$