Find and correct errors of the following mathematical expressions: (a⁸)(a⁶)=a¹⁴; ((a-b³))((a-b²)) = a² - b⁵?

The given statement (a⁸)(a⁶)=a¹⁴ is correct. When multiplying terms with the same base, we add the exponents. 8 + 6 = 14, so (a⁸)(a⁶) = a¹⁴.

The given statement ((a-b³))((a-b²)) = a² - b⁵ is incorrect. This requires expanding the expression using the FOIL method (First, Outer, Inner, Last):

(a - b³)(a - b²) = a(a) + a(-b²) + (-b³)(a) + (-b³)(-b²)
= a² - ab² - ab³ + b⁵

Therefore, the correct statement is (a - b³)(a - b²) = a² - ab² - ab³ + b⁵