Question

A student was asked to simplify this expression

A) What error(s) did the student make?
B) What is the correct simplified form of the expression?

Answer 1

Let me solve

`\\ \rm\rightarrowtail (-21x^5y^2)/(7x^4y^5)`

`\\ \rm\rightarrowtail -3x^(5-4)y^(2-5)`

`\\ \rm\rightarrowtail -3xy^(-3)`

`\\ \rm\rightarrowtail (-3x)/(y^3)`

Answer 2

`(-21x^5y^2)/(7x^4y^5)=(-21)/(7) \cdot (x^5)/(x^4) \cdot (y^2)/(y^5)`

Carry out the division of the coefficients:

`\implies -3 \cdot (x^5)/(x^4) \cdot (y^2)/(y^5)`

Apply exponent division rule
`(a^b)/(a^c)=a^(b-c)`

`\implies-3 \cdot x^(5-4) \cdot y^(2-5)`

`\implies-3 \cdot x^1 \cdot y^(-3)`

`\implies-3x y^(-3)`

(a) The student did not divide the coefficients correctly.

`(-21)/(7)=-3` NOT
`\frac13`

Also, they did not apply the exponent division rule correctly to the
`x` variable. Instead of subtracting 4 from 5 → a positive exponent, they subtracted 5 from 4 → a negative exponent.

(b)
`-3x y^(-3) \textsf{ or }-(3x)/(y^3) \textsf{ in rational form}`