Solve 5ab*(-3/4ab^2)*(-2/3ab^2c)^3

$$5 a b \cdot ( - \frac { 3 } { 4 } a b ^ { 2 } ) \cdot ( - \frac { 2 } { 3 } a b ^ { 2 } c ) ^ { 3 }$$

Evaluate

$$\frac{10c^{3}a^{5}b^{9}}{9}$$

Solution Steps

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

$$5a^{2}b\left(-\frac{3}{4}\right)b^{2}\left(-\frac{2}{3}ab^{2}c\right)^{3}$$

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

$$5a^{2}b^{3}\left(-\frac{3}{4}\right)\left(-\frac{2}{3}ab^{2}c\right)^{3}$$

Multiply 5 and -\frac{3}{4} to get -\frac{15}{4}.

$$-\frac{15}{4}a^{2}b^{3}\left(-\frac{2}{3}ab^{2}c\right)^{3}$$

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

$$-\frac{15}{4}a^{2}b^{3}\left(-\frac{2}{3}\right)^{3}a^{3}\left(b^{2}\right)^{3}c^{3}$$

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

$$-\frac{15}{4}a^{2}b^{3}\left(-\frac{2}{3}\right)^{3}a^{3}b^{6}c^{3}$$

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

$$-\frac{15}{4}a^{2}b^{3}\left(-\frac{8}{27}\right)a^{3}b^{6}c^{3}$$

Multiply -\frac{15}{4} and -\frac{8}{27} to get \frac{10}{9}.

$$\frac{10}{9}a^{2}b^{3}a^{3}b^{6}c^{3}$$

To multiply powers of the same base, add their exponents. Add 2 and 3 to get 5.

$$\frac{10}{9}a^{5}b^{3}b^{6}c^{3}$$

To multiply powers of the same base, add their exponents. Add 3 and 6 to get 9.

$$\frac{10}{9}a^{5}b^{9}c^{3}$$

Expand

$$\frac{10c^{3}a^{5}b^{9}}{9}$$

Solution Steps

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

$$5a^{2}b\left(-\frac{3}{4}\right)b^{2}\left(-\frac{2}{3}ab^{2}c\right)^{3}$$

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

$$5a^{2}b^{3}\left(-\frac{3}{4}\right)\left(-\frac{2}{3}ab^{2}c\right)^{3}$$

Multiply 5 and -\frac{3}{4} to get -\frac{15}{4}.

$$-\frac{15}{4}a^{2}b^{3}\left(-\frac{2}{3}ab^{2}c\right)^{3}$$

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

$$-\frac{15}{4}a^{2}b^{3}\left(-\frac{2}{3}\right)^{3}a^{3}\left(b^{2}\right)^{3}c^{3}$$

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

$$-\frac{15}{4}a^{2}b^{3}\left(-\frac{2}{3}\right)^{3}a^{3}b^{6}c^{3}$$

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

$$-\frac{15}{4}a^{2}b^{3}\left(-\frac{8}{27}\right)a^{3}b^{6}c^{3}$$

Multiply -\frac{15}{4} and -\frac{8}{27} to get \frac{10}{9}.

$$\frac{10}{9}a^{2}b^{3}a^{3}b^{6}c^{3}$$

To multiply powers of the same base, add their exponents. Add 2 and 3 to get 5.

$$\frac{10}{9}a^{5}b^{3}b^{6}c^{3}$$

To multiply powers of the same base, add their exponents. Add 3 and 6 to get 9.

$$\frac{10}{9}a^{5}b^{9}c^{3}$$