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

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

Evaluate

$$\frac{4\times \left(\frac{b}{c}\right)^{2}a^{4}}{9}$$

Solution Steps

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

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

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

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

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

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

Calculate -2 to the power of 2 and get 4.

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

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

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

Calculate 3 to the power of 2 and get 9.

$$\frac{4a^{4}b^{2}}{9c^{2}}$$

Expand

$$\frac{4\times \left(\frac{b}{c}\right)^{2}a^{4}}{9}$$

Solution Steps

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

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

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

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

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

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

Calculate -2 to the power of 2 and get 4.

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

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

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

Calculate 3 to the power of 2 and get 9.

$$\frac{4a^{4}b^{2}}{9c^{2}}$$