Solve (a^-4/3a^2b^-1)^2

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

Evaluate

$$\frac{b^{2}}{9a^{12}}$$

Solution Steps

To divide powers of the same base, subtract the numerator's exponent from the denominator's exponent.

$$\left(\frac{1}{3\times \frac{1}{b}a^{6}}\right)^{2}$$

Express 3\times \frac{1}{b} as a single fraction.

$$\left(\frac{1}{\frac{3}{b}a^{6}}\right)^{2}$$

Express \frac{3}{b}a^{6} as a single fraction.

$$\left(\frac{1}{\frac{3a^{6}}{b}}\right)^{2}$$

Divide 1 by \frac{3a^{6}}{b} by multiplying 1 by the reciprocal of \frac{3a^{6}}{b}.

$$\left(\frac{b}{3a^{6}}\right)^{2}$$

To raise \frac{b}{3a^{6}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{b^{2}}{\left(3a^{6}\right)^{2}}$$

Expand \left(3a^{6}\right)^{2}.

$$\frac{b^{2}}{3^{2}\left(a^{6}\right)^{2}}$$

To raise a power to another power, multiply the exponents. Multiply 6 and 2 to get 12.

$$\frac{b^{2}}{3^{2}a^{12}}$$

Calculate 3 to the power of 2 and get 9.

$$\frac{b^{2}}{9a^{12}}$$

Expand

$$\frac{b^{2}}{9a^{12}}$$

Solution Steps

To divide powers of the same base, subtract the numerator's exponent from the denominator's exponent.

$$\left(\frac{1}{3\times \frac{1}{b}a^{6}}\right)^{2}$$

Express 3\times \frac{1}{b} as a single fraction.

$$\left(\frac{1}{\frac{3}{b}a^{6}}\right)^{2}$$

Express \frac{3}{b}a^{6} as a single fraction.

$$\left(\frac{1}{\frac{3a^{6}}{b}}\right)^{2}$$

Divide 1 by \frac{3a^{6}}{b} by multiplying 1 by the reciprocal of \frac{3a^{6}}{b}.

$$\left(\frac{b}{3a^{6}}\right)^{2}$$

To raise \frac{b}{3a^{6}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{b^{2}}{\left(3a^{6}\right)^{2}}$$

Expand \left(3a^{6}\right)^{2}.

$$\frac{b^{2}}{3^{2}\left(a^{6}\right)^{2}}$$

To raise a power to another power, multiply the exponents. Multiply 6 and 2 to get 12.

$$\frac{b^{2}}{3^{2}a^{12}}$$

Calculate 3 to the power of 2 and get 9.

$$\frac{b^{2}}{9a^{12}}$$