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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?

A student was asked to simplify this expression A) What error(s) did the student make-example-1
User Exos
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2 Answers

8 votes

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)

User Cmather
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8 votes

Answer:


(-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}

User Amjad Sahi
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