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

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

Evaluate

$$\frac{9b^{6}}{4a^{4}}$$

Solution Steps

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Expand

$$\frac{9b^{6}}{4a^{4}}$$

Solution Steps

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

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

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

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

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

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

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

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

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

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

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

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

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

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