Solve ((4x^-2)^-28x^-2)^-1

$$( ( 4 x ^ { - 2 } ) ^ { - 2 } 8 x ^ { - 2 } ) ^ { - 1 }$$

Evaluate

$$\frac{2}{x^{2}}$$

Solution Steps

Expand \left(4x^{-2}\right)^{-2}.

$$\left(4^{-2}\left(x^{-2}\right)^{-2}\times 8x^{-2}\right)^{-1}$$

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

$$\left(4^{-2}x^{4}\times 8x^{-2}\right)^{-1}$$

Calculate 4 to the power of -2 and get \frac{1}{16}.

$$\left(\frac{1}{16}x^{4}\times 8x^{-2}\right)^{-1}$$

Multiply \frac{1}{16} and 8 to get \frac{1}{2}.

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

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

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

Expand \left(\frac{1}{2}x^{2}\right)^{-1}.

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

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

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

Calculate \frac{1}{2} to the power of -1 and get 2.

$$2x^{-2}$$

Expand

$$\frac{2}{x^{2}}$$

Solution Steps

Expand \left(4x^{-2}\right)^{-2}.

$$\left(4^{-2}\left(x^{-2}\right)^{-2}\times 8x^{-2}\right)^{-1}$$

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

$$\left(4^{-2}x^{4}\times 8x^{-2}\right)^{-1}$$

Calculate 4 to the power of -2 and get \frac{1}{16}.

$$\left(\frac{1}{16}x^{4}\times 8x^{-2}\right)^{-1}$$

Multiply \frac{1}{16} and 8 to get \frac{1}{2}.

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

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

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

Expand \left(\frac{1}{2}x^{2}\right)^{-1}.

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

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

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

Calculate \frac{1}{2} to the power of -1 and get 2.

$$2x^{-2}$$