Solve 6a^2b^3*(-1/3a^3)^3

$$6 a ^ { 2 } b ^ { 3 } \cdot ( - \frac { 1 } { 3 } a ^ { 3 } ) ^ { 3 }$$

Evaluate

$$-\frac{2b^{3}a^{11}}{9}$$

Solution Steps

Expand \left(-\frac{1}{3}a^{3}\right)^{3}.

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

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

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

Calculate -\frac{1}{3} to the power of 3 and get -\frac{1}{27}.

$$6a^{2}b^{3}\left(-\frac{1}{27}\right)a^{9}$$

Multiply 6 and -\frac{1}{27} to get -\frac{2}{9}.

$$-\frac{2}{9}a^{2}b^{3}a^{9}$$

To multiply powers of the same base, add their exponents. Add 2 and 9 to get 11.

$$-\frac{2}{9}a^{11}b^{3}$$

Expand

$$-\frac{2b^{3}a^{11}}{9}$$

Solution Steps

Expand \left(-\frac{1}{3}a^{3}\right)^{3}.

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

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

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

Calculate -\frac{1}{3} to the power of 3 and get -\frac{1}{27}.

$$6a^{2}b^{3}\left(-\frac{1}{27}\right)a^{9}$$

Multiply 6 and -\frac{1}{27} to get -\frac{2}{9}.

$$-\frac{2}{9}a^{2}b^{3}a^{9}$$

To multiply powers of the same base, add their exponents. Add 2 and 9 to get 11.

$$-\frac{2}{9}a^{11}b^{3}$$