Solve (a^-2/a^5)^-2

$$( a ^ { - 2 } / a ^ { 5 } ) ^ { - 2 }$$

Evaluate

$$a^{14}$$

Solution Steps

Rewrite a^{5} as a^{-2}a^{7}. Cancel out a^{-2} in both numerator and denominator.

$$\left(\frac{1}{a^{7}}\right)^{-2}$$

To raise \frac{1}{a^{7}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{1^{-2}}{\left(a^{7}\right)^{-2}}$$

To raise a power to another power, multiply the exponents. Multiply 7 and -2 to get -14.

$$\frac{1^{-2}}{a^{-14}}$$

Calculate 1 to the power of -2 and get 1.

$$\frac{1}{a^{-14}}$$

Expand

$$a^{14}$$

Solution Steps

Rewrite a^{5} as a^{-2}a^{7}. Cancel out a^{-2} in both numerator and denominator.

$$\left(\frac{1}{a^{7}}\right)^{-2}$$

To raise \frac{1}{a^{7}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{1^{-2}}{\left(a^{7}\right)^{-2}}$$

To raise a power to another power, multiply the exponents. Multiply 7 and -2 to get -14.

$$\frac{1^{-2}}{a^{-14}}$$

Calculate 1 to the power of -2 and get 1.

$$\frac{1}{a^{-14}}$$