What is the equivalent pair to 1/x^2

Question

1
x^-2
((x^2) x (x^-2)
x^10
(x^2) / (x^8)
1/x^6
(x^2) × (x^8)

Answer 1

To find the equivalent expression for \( \frac{1}{x^2} \), we will analyze each option:

1. \( 1 \) - Not equivalent.
2. \( x^{-2} \) - Equivalent since \( \frac{1}{x^2} = x^{-2} \).
3. \( ((x^2) \cdot (x^{-2})) \) - This simplifies to \( x^{2 - 2} = x^0 = 1 \), so not equivalent.
4. \( x^{10} \) - Not equivalent.
5. \( \frac{x^2}{x^8} \) - This simplifies to \( x^{2-8} = x^{-6} \), so not equivalent.
6. \( \frac{1}{x^6} \) - Not equivalent.
7. \( (x^2) \cdot (x^8) \) - This simplifies to \( x^{2+8} = x^{10} \), so not equivalent.

The only equivalent expression to \( \frac{1}{x^2} \) from the given options is:

\( x^{-2} \).