Question
Now we have a pattern that works quite well if the exponent in the numerator is greater than that of the
denominator. But does it work if that isn't true?
Exercise #5: Rewrite each of the following expressions two ways: (i) by using the exponent rule developed in
#4(d) and (ii) by simplifying using techniques we have seen in the last lesson.
(a)
(b)
56
(c) =
Answer
(a) (i) (2x^3)^2/2x^2 = 4x^6/2x^2 = 2x^4 (ii) (2x^3)^2/2x^2 = (2x^2 * 2x)^2/2x^2 = 4x^4/2x^2 = 2x^4; (b) (i) 56^2/56^3 = 56/56^2 = 1/56 (ii) 56^2/56^3 = (7*8)^2/7^3*8 = 64/56^3 = 1/56; (c) (i) (3x^2y^3)^4/3x^3y^2 = 81x^8y^12/3x^3y^2 = 27x^5y^10 (ii) (3x^2y^3)^4/3x^3y^2 = (3x^2 * y^3)^4/3x^3y^2 = 27x^4y^12/3x^3y^2 = 27x^5y^10.