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

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

Evaluate

$$\frac{b^{2}}{4a^{4}}$$

Solution Steps

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

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

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

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

Calculate b to the power of 1 and get b.

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

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

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

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

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

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

$$\frac{b^{2}}{2^{2}a^{4}}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{b^{2}}{4a^{4}}$$

Expand

$$\frac{b^{2}}{4a^{4}}$$

Solution Steps

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

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

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

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

Calculate b to the power of 1 and get b.

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

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

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

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

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

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

$$\frac{b^{2}}{2^{2}a^{4}}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{b^{2}}{4a^{4}}$$