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

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

Evaluate

$$\left(\frac{b}{a}\right)^{10}$$

Solution Steps

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

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

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

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

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

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

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

$$\frac{b^{10}}{\left(a^{5}\right)^{2}}$$

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

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

Expand

$$\left(\frac{b}{a}\right)^{10}$$

Solution Steps

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

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

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

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

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

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

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

$$\frac{b^{10}}{\left(a^{5}\right)^{2}}$$

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

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