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

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

Evaluate

$$\frac{b^{6}}{a^{10}}$$

Solution Steps

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

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

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

$$\left(\frac{b^{3}}{a^{5}}\right)^{2}$$

To raise \frac{b^{3}}{a^{5}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(b^{3}\right)^{2}}{\left(a^{5}\right)^{2}}$$

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

$$\frac{b^{6}}{\left(a^{5}\right)^{2}}$$

To raise a power to another power, multiply the exponents. Multiply 5 and 2 to get 10.

$$\frac{b^{6}}{a^{10}}$$

Expand

$$\frac{b^{6}}{a^{10}}$$

Solution Steps

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

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

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

$$\left(\frac{b^{3}}{a^{5}}\right)^{2}$$

To raise \frac{b^{3}}{a^{5}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(b^{3}\right)^{2}}{\left(a^{5}\right)^{2}}$$

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

$$\frac{b^{6}}{\left(a^{5}\right)^{2}}$$

To raise a power to another power, multiply the exponents. Multiply 5 and 2 to get 10.

$$\frac{b^{6}}{a^{10}}$$