Question

Blake simplified the expression (x^12/x^-3)^5 to 1/x^20. What was Blake’s mistake

A)He added 5 to the exponent in the numerator instead of multiplying.
B)He subtracted the exponents in the parentheses instead of dividing.
C)He multiplied only the exponent in the numerator of the fraction by 5.
D)He divided the exponents in the parentheses instead of subtracting.

Answer 1

D

Explanation:

Answer 2

Below are the steps that need to be performed to this expression to obtain the correct answer.

`((x^(12))/(x^(-3)))^(5)\\=(x^(60))/(x^(-15)) \\= x^(60+15)\\=x^(75)`

If, instead of multiply the exponents of both the numerator and denominator by 5 before proceeding, you divide the exponents and then multiply by 5, you will obtain:

`((x^(12))/(x^(-3)))^(5) \\=(x^(12/-3))^(5)\\=(x^(-4))^(5)\\=x^(-20)`

Which can be written, in positive exponents, as

`(1)/(x^(20))`.

So Blake's mistake is that he divided the exponents inside the parenthesis before proceeding. Answer choice D is the right answer.

ANSWER: D