The value of [(.253*.253-.253*.067+.067*.067)/(.253*.253*.253+.067*.067*.067)] is:

Given:

\(\dfrac{(.253 \times .253 - .253 \times .067 + .067 \times .067)}{(.253 \times .253 \times .253 + .067 \times .067 \times .067)}\)

Formula used:

\(\dfrac{a^2 - ab + b^2}{a^3 + b^3}\) = \(\dfrac{{a^2 - ab + b^2}}{(a + b)(a^2 - ab + b^2)}\) = \(\dfrac{1}{a + b}\)

Calculation:

Let a = 0.253 and b = 0.067

⇒ \(\dfrac{{(0.253^2 - 0.253 \times 0.067 + 0.067^2)}}{(0.253 + 0.067)(0.253^2 - 0.253 \times 0.067 + 0.067^2)}\)

⇒ \(\dfrac{1}{0.253 + 0.067}\) = (1 / 0.32)

⇒ \(\)3.125

∴ The value of the given expression is 3.125.