Solve (b^-11/4/a^-1/2)^8

$$( \frac { b ^ { - 11 / 4 } } { a ^ { - 1 / 2 } } ) ^ { 8 }$$

Evaluate

$$\frac{a^{4}}{b^{22}}$$

Solution Steps

To raise \frac{b^{-\frac{11}{4}}}{a^{-\frac{1}{2}}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(b^{-\frac{11}{4}}\right)^{8}}{\left(a^{-\frac{1}{2}}\right)^{8}}$$

To raise a power to another power, multiply the exponents. Multiply -\frac{11}{4} and 8 to get -22.

$$\frac{b^{-22}}{\left(a^{-\frac{1}{2}}\right)^{8}}$$

To raise a power to another power, multiply the exponents. Multiply -\frac{1}{2} and 8 to get -4.

$$\frac{b^{-22}}{a^{-4}}$$

Expand

$$\frac{a^{4}}{b^{22}}$$

Solution Steps

To raise \frac{b^{-\frac{11}{4}}}{a^{-\frac{1}{2}}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(b^{-\frac{11}{4}}\right)^{8}}{\left(a^{-\frac{1}{2}}\right)^{8}}$$

To raise a power to another power, multiply the exponents. Multiply -\frac{11}{4} and 8 to get -22.

$$\frac{b^{-22}}{\left(a^{-\frac{1}{2}}\right)^{8}}$$

To raise a power to another power, multiply the exponents. Multiply -\frac{1}{2} and 8 to get -4.

$$\frac{b^{-22}}{a^{-4}}$$