The number 75600 can be factorised as ${\mathrm{a}}^1\times {\mathrm{b}}^2\times {\mathrm{c}}^3\times {\mathrm{d}}^4$. What is the value of (a + c)? 

According to the fundamental theorem of arithmetic, every number can be factorised as a product of its primes in a unique way. 

Therefore, the number 75600 can be prime-factorised as 

75600 = 2 × 2 × 2 × 2 × 3 × 3 × 3 × 5 × 5 × 7 

              = 2⁴ × 3³ × 5² × 7¹ 

On comparing it to (a¹ × b² × c³ × d⁴), we obtain 

a = 7, b = 5, c = 3 and d = 2 

Thus, the value of (a + c) is (7 + 3) = 10.