Each of the following solutions contains at least one error.

Question

Each of the following solutions contains at least one error. Provide a correct solution to each question and EXPLAIN (in words) the error that was made. Use proper mathematical language in your explanations.

a) 4^(0)=0

b) (-5)^(-2)=25

c) (6x^(2))/(2x^(2) )=4x

d) Factor 9x^(2)-25 The student’s answer is (3x-5)^(2)

Answer 1

a) anything to the 0 power = 1. (unless the base is zero, then it's undefined) x^0 = 1 unless x=0

4^0 = 1, not 0. 1 = b^x/b^x = b^(x-x) = b^0 = 1

b) (-5)^(-2) = 1/(-5)^2 = 1/25 not 25. the negative exponent switches the base to the denominator. b^-x = 1/(b^x)

c) 6x^2/2x^2 = 6/2 = 3, not 4x. the x^2 cancels in denominator and numerator

d) 9x^2 -25 = (3x+5)(3x-5), not (3x-5)^2. the general formula is (a^2-b^2) = (a+b)(a-b), and a= 9x, b= 5

(3x-5)^2 = 9x^2 -30x +25, not 9x^2 -25