Solve alpha(a^2b^-1/a^-2b)^2

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

Evaluate

$$\frac{\alpha a^{8}}{b^{4}}$$

Solution Steps

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

$$\alpha \times \left(\frac{\frac{1}{b}a^{4}}{b}\right)^{2}$$

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

$$\alpha \times \left(\frac{a^{4}}{b^{2}}\right)^{2}$$

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

$$\alpha \times \frac{\left(a^{4}\right)^{2}}{\left(b^{2}\right)^{2}}$$

Express \alpha \times \frac{\left(a^{4}\right)^{2}}{\left(b^{2}\right)^{2}} as a single fraction.

$$\frac{\alpha \left(a^{4}\right)^{2}}{\left(b^{2}\right)^{2}}$$

To raise a power to another power, multiply the exponents. Multiply 4 and 2 to get 8.

$$\frac{\alpha a^{8}}{\left(b^{2}\right)^{2}}$$

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

$$\frac{\alpha a^{8}}{b^{4}}$$

Expand

$$\frac{\alpha a^{8}}{b^{4}}$$

Solution Steps

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

$$\alpha \times \left(\frac{\frac{1}{b}a^{4}}{b}\right)^{2}$$

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

$$\alpha \times \left(\frac{a^{4}}{b^{2}}\right)^{2}$$

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

$$\alpha \times \frac{\left(a^{4}\right)^{2}}{\left(b^{2}\right)^{2}}$$

Express \alpha \times \frac{\left(a^{4}\right)^{2}}{\left(b^{2}\right)^{2}} as a single fraction.

$$\frac{\alpha \left(a^{4}\right)^{2}}{\left(b^{2}\right)^{2}}$$

To raise a power to another power, multiply the exponents. Multiply 4 and 2 to get 8.

$$\frac{\alpha a^{8}}{\left(b^{2}\right)^{2}}$$

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

$$\frac{\alpha a^{8}}{b^{4}}$$