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

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

Evaluate

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

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 \frac{1}{4}.

$$\frac{\frac{1}{4}a^{-4}b^{-2}}{\left(3c\right)^{-2}}$$

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

$$\frac{\frac{1}{4}a^{-4}b^{-2}}{3^{-2}c^{-2}}$$

Calculate 3 to the power of -2 and get \frac{1}{9}.

$$\frac{\frac{1}{4}a^{-4}b^{-2}}{\frac{1}{9}c^{-2}}$$

Expand

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

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 \frac{1}{4}.

$$\frac{\frac{1}{4}a^{-4}b^{-2}}{\left(3c\right)^{-2}}$$

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

$$\frac{\frac{1}{4}a^{-4}b^{-2}}{3^{-2}c^{-2}}$$

Calculate 3 to the power of -2 and get \frac{1}{9}.

$$\frac{\frac{1}{4}a^{-4}b^{-2}}{\frac{1}{9}c^{-2}}$$