The area of a square can be represented by the expression x10. The side of the square can be written in the form xn. What is the value of n?

The answer is n = 5.

Area (A) of the square can be expressed as:

A = a²

where a is the side of the square.

It is given:

A = x¹⁰

a = xⁿ

Therefore

x¹⁰ = (xⁿ) ² = xⁿ*² = x²ⁿ

x¹⁰ = x²ⁿ

Let's logarithm both sides of the equation:

log (x¹⁰) = log (x²ⁿ)

⇒ 10 * log (x) = 2n * log (x)

Divide both sides of the equation by log (x):

10 * log (x) / log (x) = 2n * log (x) / log (x)

10 * 1 = 2n * 1

10 = 2n

⇒ n = 10 : 2 = 5