Solve (-2a^2b/3c)^3

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

Evaluate

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

Solution Steps

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

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

Expand \left(-2a^{2}b\right)^{3}.

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

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

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

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

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

Expand \left(3c\right)^{3}.

$$\frac{-8a^{6}b^{3}}{3^{3}c^{3}}$$

Calculate 3 to the power of 3 and get 27.

$$\frac{-8a^{6}b^{3}}{27c^{3}}$$

Expand

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

Solution Steps

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

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

Expand \left(-2a^{2}b\right)^{3}.

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

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

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

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

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

Expand \left(3c\right)^{3}.

$$\frac{-8a^{6}b^{3}}{3^{3}c^{3}}$$

Calculate 3 to the power of 3 and get 27.

$$\frac{-8a^{6}b^{3}}{27c^{3}}$$