Question 3 on the OCR MEI C1 June 2015 paper. Evaluate the following. (i) 200^0 (ii) (9/25)^(-1/2)

For both parts you have to remember some of the properties of powers. Rule 1: x^0 = 1. Rule 2: x^(-n) = 1/(x^n). Rule 3: x^(1/n) = n-th root of x. For part (i) we can use rule 1 to see that 200^0 = 0. For part (ii) we can first rewrite (9/25)^(-½) as (9/25) ^ (-1) * (½) = ((9/25) ^ (-1) ) ^ (½). Using rule 2 to evaluate the negative power we can see ((9/25) ^ (-1) )^ (½) = ((25/9) )^ (½). Using rule 3 we can see ((25/9) )^ (½) = 5/3. If the student finds this difficult, I would take the opportunity to revisit other properties of powers like x^(m+n) = x^m * x^n. Once I had explained the concepts I would use another example like (8/27)^(-1/3) to see if the student now understands it better.