Solve frac{(x^{-1})^{2}*(x^2)^-2}{(x^-2)^3}

$$\frac { ( x ^ { - 1 } ) ^ { 2 } \times ( x ^ { 2 } ) ^ { - 2 } } { ( x ^ { - 2 } ) ^ { 3 } }$$

Evaluate

$$1$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply -1 and 2 to get -2.

$$\frac{x^{-2}\left(x^{2}\right)^{-2}}{\left(x^{-2}\right)^{3}}$$

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

$$\frac{x^{-2}x^{-4}}{\left(x^{-2}\right)^{3}}$$

To multiply powers of the same base, add their exponents. Add -2 and -4 to get -6.

$$\frac{x^{-6}}{\left(x^{-2}\right)^{3}}$$

To raise a power to another power, multiply the exponents. Multiply -2 and 3 to get -6.

$$\frac{x^{-6}}{x^{-6}}$$

Divide x^{-6} by x^{-6} to get 1.

$$1$$

Factor

$$1$$