Solve (frac{-2a^{3}b^{2}c^{4}}{3a^2b^3c^7})^-2

$$( \frac { - 2 a ^ { 3 } b ^ { 2 } c ^ { 4 } } { 3 a ^ { 2 } b ^ { 3 } c ^ { 7 } } ) ^ { - 2 }$$

Evaluate

$$\frac{9\times \left(\frac{b}{a}\right)^{2}c^{6}}{4}$$

Solution Steps

Cancel out a^{2}b^{2}c^{4} in both numerator and denominator.

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

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

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

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

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

Calculate -2 to the power of -2 and get \frac{1}{4}.

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

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

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

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

$$\frac{\frac{1}{4}a^{-2}}{3^{-2}b^{-2}c^{-6}}$$

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

$$\frac{\frac{1}{4}a^{-2}}{\frac{1}{9}b^{-2}c^{-6}}$$

Expand

$$\frac{9\times \left(\frac{b}{a}\right)^{2}c^{6}}{4}$$

Solution Steps

Cancel out a^{2}b^{2}c^{4} in both numerator and denominator.

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

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

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

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

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

Calculate -2 to the power of -2 and get \frac{1}{4}.

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

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

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

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

$$\frac{\frac{1}{4}a^{-2}}{3^{-2}b^{-2}c^{-6}}$$

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

$$\frac{\frac{1}{4}a^{-2}}{\frac{1}{9}b^{-2}c^{-6}}$$