Question 1

A chemist is preparing a solution and needs to divide $x^8y^5$ by $x^3y^2$. What is the simplified form of the expression?

Accepted Answer

$x^{5}y^{3}$

Question 2

Simplify the following expression, which represents the ratio of two populations: $\dfrac{12a^7b^4}{3a^3b^2}$.

Accepted Answer

$4a^{4}b^{2}$

Question 3

A biologist is comparing the growth of two bacteria cultures, represented by $\dfrac{18x^5y^3}{6x^2y}$. What is the simplified form?

Accepted Answer

$3x^{3}y^{2}$

Question 4

Simplify $\dfrac{(-24m^6n^4)}{8m^2n}$, which could represent the ratio of two chemical concentrations.

Accepted Answer

$-3m^{4}n^{3}$

Question 5

A physics formula involves dividing $x^7y^2$ by $x^4y^5$. What is the simplified result?

Accepted Answer

$x^{3}y^{-3}$

Question 6

Simplify $\dfrac{15a^5b^3}{-5a^2b}$, which could represent the ratio of two rates in economics.

Accepted Answer

$-3a^{3}b^{2}$

Question 7

A medical researcher divides $x^4y^6z^2$ by $2x^2y^3z$. What is the simplified form?

Accepted Answer

$\dfrac{1}{2}x^{2}y^{3}z$

Question 8

Simplify $\dfrac{(-18x^5y^2)}{6x^2y^4}$, which could represent the ratio of two forces.

Accepted Answer

$-3x^{3}y^{-2}$

Question 9

A company’s profit model involves $\dfrac{36m^9n^5}{12m^3n^2}$. What is the simplified expression?

Accepted Answer

$3m^{6}n^{3}$

Question 10

Simplify $\dfrac{8a^4b^2}{-2a^2b}$, which could represent the ratio of two electrical currents.

Accepted Answer

$-4a^{2}b$

Question 11

A population model uses $\dfrac{27x^5y^3}{9x^2y^2}$. What is the simplified form?

Accepted Answer

$3x^{3}y$

Question 12

Simplify $\dfrac{(-30m^7n^4)}{15m^2n^2}$, which could represent the ratio of two chemical reaction rates.

Accepted Answer

$-2m^{5}n^{2}$

Question 13

A physics equation involves $\dfrac{18x^6y^3}{-6x^2y}$. What is the simplified result?

Accepted Answer

$-3x^{4}y^{2}$

Question 14

Simplify $\dfrac{45a^8b^5}{15a^3b^2}$, which could represent the ratio of two investment returns.

Accepted Answer

$3a^{5}b^{3}$

Question 15

A biologist divides $-24x^5y^3$ by $8x^2y$. What is the simplified form?

Accepted Answer

$-3x^{3}y^{2}$

Question 16

Simplify $\dfrac{54m^6n^4}{18m^2n}$, which could represent the ratio of two rates in a chemical process.

Accepted Answer

$3m^{4}n^{3}$

Question 17

A company’s cost function involves $\dfrac{20x^7y^4}{4x^2y^2}$. What is the simplified expression?

Accepted Answer

$5x^{5}y^{2}$

Question 18

Simplify $\dfrac{-36a^9b^6}{12a^3b^2}$, which could represent the ratio of two energy outputs.

Accepted Answer

$-3a^{6}b^{4}$

Question 19

A researcher divides $-18x^5y^2$ by $6x^2y^4$. What is the simplified form?

Accepted Answer

$-3x^{3}y^{-2}$

Question 20

Simplify $\dfrac{21m^8n^5}{7m^2n^2}$, which could represent the ratio of two populations.

Accepted Answer

$3m^{6}n^{3}$

Step-by-Step Guidance: Dividing Monomials (College Algebra)

Study Guide - Practice Questions