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

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

Evaluate

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

Solution Steps

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

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

Calculate -1 to the power of -2 and get 1.

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

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

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

Express 1\times \frac{\left(2a^{2}b^{-2}\right)^{-2}}{\left(3x^{-3}\right)^{-2}} as a single fraction.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Expand

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

Solution Steps

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

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

Calculate -1 to the power of -2 and get 1.

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

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

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

Express 1\times \frac{\left(2a^{2}b^{-2}\right)^{-2}}{\left(3x^{-3}\right)^{-2}} as a single fraction.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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