Which expression is a valid simplification of (1 - x/(x+blah))^20?

• A. (1 - x/(x+blah))^20
• B. (blah/(x+blah))^20
• C. (x+blah - x)/(x+blah)^20
• D. (blah/(x+blah))^10

Answer: (B)

Simplifying the expression inside the parentheses first is the key. Rewrite 1 as (x+blah)/(x+blah) and subtract x/(x+blah): 1 − x/(x+blah) = [(x+blah) − x]/(x+blah) = blah/(x+blah). Then raise that whole fraction to the 20th power, giving (blah/(x+blah))^20. This is the correct simplification because the exponent applies to the entire fraction, not just the numerator or the denominator separately.

Other forms don’t match because splitting the exponent across the denominator or reducing the power to 10 changes the value. For example, blah/(x+blah)^20 would be different from (blah)^{20}/(x+blah)^{20}, and taking the power 10 would give a different overall exponent. The clean, correct result is (blah/(x+blah))^20, assuming x+blah ≠ 0.