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

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

Evaluate

$$-\frac{256a^{3}b^{6}c^{9}}{27}$$

Solution Steps

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

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

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

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

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

$$4\left(-\frac{4}{3}\right)^{3}a^{3}b^{6}c^{9}$$

Calculate -\frac{4}{3} to the power of 3 and get -\frac{64}{27}.

$$4\left(-\frac{64}{27}\right)a^{3}b^{6}c^{9}$$

Multiply 4 and -\frac{64}{27} to get -\frac{256}{27}.

$$-\frac{256}{27}a^{3}b^{6}c^{9}$$

Expand

$$-\frac{256a^{3}b^{6}c^{9}}{27}$$

Solution Steps

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

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

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

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

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

$$4\left(-\frac{4}{3}\right)^{3}a^{3}b^{6}c^{9}$$

Calculate -\frac{4}{3} to the power of 3 and get -\frac{64}{27}.

$$4\left(-\frac{64}{27}\right)a^{3}b^{6}c^{9}$$

Multiply 4 and -\frac{64}{27} to get -\frac{256}{27}.

$$-\frac{256}{27}a^{3}b^{6}c^{9}$$