Question

It seems like Jerry answered a question incorrectly. By what term should jerry divide his answer to get the correct like term?

• A. $x^2{z}^3$
• B. $x^3{y}^2{z}^4$
• C. $x^2{y}^1{z}^3$
• D. $x^3{y}^1{z}^4$

Answer 1

The correct option is D $x^3{y}^1{z}^4$

Jerry needs a like term of the $9x^5{y}^8{z}^7$.
Instead, he writes $2x^8{y}^9{z}^{11}$.

Jerry needs a term in which the powers of the variables are as follows:
x: 5
y: 8
z: 7

Let's assume that Jerry is dividing his written expression $(2x^8{y}^9{z}^{11}).$Now, the obtained term is a like term of $x^a{y}^b{z}^{\mathrm{c.}}$

$2x^8{y}^9{z}^{11}÷x^a{y}^b{z}^c=2x^{\left(\mathrm{8\; –}a\right)}{y}^{\left(\mathrm{9\; –}b\right)}{z}^{\left(\mathrm{11\; –}c\right)}$
Now, if the obtained term is a like term of $9x^5{y}^8{z}^7$, the exponents should be equal.

Hence,
8 – a = 5 --> a = 3
9 – b = 8 --> b = 1
11 – c = 7 --> c = 4


So, Jerry should divide his expression with $x^3{y}^1{z}^4$