Use Rational exponents to write as a single radical expression. Assume that all variables represent positive real numbers

Question

Use Rational exponents to write as a single radical expression. Assume that all variables represent positive real numbers. I have tried to find steps for this equation, but have only found the answer; ⁶⁰√x⁴⁷

I'm almost completely sure that the 60 comes from the LCD between 5, 6, and 12. I'm still confused on how we get 47. Any help on this is more than appreciated!

⁶√x * ⁵√x * ¹²√x⁵

Answer 1

x^(1/6) + x^(1/5) + x^(5/12)

= x^(10/60) + x^(12/60) + x^(25/60)

= x^(10/60 + 12/60 + 25/60)

= x^(47/60)

= 0060th root of x^47 but that's wrong. You calculated the product not the sum. product is found by summing the exponents when the base is the same

2^2 times 2^3 = 2^(2+3) = 2^5 = 32 = 4x8

but 2^2 + 2^3 does Not = 32. It =4+8= 12

16^(1/2) + 16^(1/4) = 4 +2 =6 = 36^(1/2)

combines 2 radicals with same base into 1 radical,