Solve -(11/3ab^2c^3)^3

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

Evaluate

$$-\frac{64a^{3}b^{6}c^{9}}{27}$$

Solution Steps

Multiply 1 and 3 to get 3.

$$-\left(\frac{3+1}{3}ab^{2}c^{3}\right)^{3}$$

Add 3 and 1 to get 4.

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

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

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

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

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

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

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

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

$$-\frac{64}{27}a^{3}b^{6}c^{9}$$

Expand

$$-\frac{64a^{3}b^{6}c^{9}}{27}$$

Solution Steps

Multiply 1 and 3 to get 3.

$$-\left(\frac{3+1}{3}ab^{2}c^{3}\right)^{3}$$

Add 3 and 1 to get 4.

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

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

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

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

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

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

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

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

$$-\frac{64}{27}a^{3}b^{6}c^{9}$$