To simplify this trigonometric expression, we can use the double angle formula for cosine:

cos(2θ) = 2cos^2(θ) - 1

Let's first simplify the expression cos^2(13π/24) * cos^2(23π/24):

= cos(213π/24) cos(223π/24)
= cos(13π/12) cos(23π/12)
= 2cos(13π/12)cos(23π/12) - 1

Now, we can use the sum-to-product identities for cosine:

cos(A)cos(B) = 1/2[cos(A+B) + cos(A-B)]

Applying this formula, we get:

2cos(13π/12)cos(23π/12)
= 2[1/2(cos(13π/12 + 23π/12) + cos(13π/12 - 23π/12)]
= 2[1/2(cos(2π) + cos(-10π/12))]
= 2[1/2(1 + cos(-5π/6))]
= 2[1/2(1 + cos(5π/6))]
= 2[1/2(1 + -√3/2)]
= 2[1/2(1 - √3/2)]
= 2[1/2 - √3/4]
= 1 - √3/2

Therefore, the simplified expression is 1 - √3/2.