Solve (x^-15/x^-13)^4

$$( \frac { x ^ { - 15 } } { x ^ { - 13 } } ) ^ { 4 }$$

Evaluate

$$\frac{1}{x^{8}}$$

Solution Steps

Rewrite x^{-13} as x^{-15}x^{2}. Cancel out x^{-15} in both numerator and denominator.

$$\left(\frac{1}{x^{2}}\right)^{4}$$

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

$$\frac{1^{4}}{\left(x^{2}\right)^{4}}$$

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

$$\frac{1^{4}}{x^{8}}$$

Calculate 1 to the power of 4 and get 1.

$$\frac{1}{x^{8}}$$

Expand

$$\frac{1}{x^{8}}$$

Solution Steps

Rewrite x^{-13} as x^{-15}x^{2}. Cancel out x^{-15} in both numerator and denominator.

$$\left(\frac{1}{x^{2}}\right)^{4}$$

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

$$\frac{1^{4}}{\left(x^{2}\right)^{4}}$$

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

$$\frac{1^{4}}{x^{8}}$$

Calculate 1 to the power of 4 and get 1.

$$\frac{1}{x^{8}}$$