Question 1

Which of the following correctly applies the quotient rule to simplify $$\frac{a^7$}{a^3$}$$?

Accepted Answer

$$a^{4}$$

Question 2

Simplify $$\frac{5^0$}{2^0$}$$ using the zero-exponent rule.

Accepted Answer

$$1$$

Question 3

Which expression is equivalent to $$\left(\frac{x^2$}{y^3$}\$$right)^4$$ using the quotients-to-powers rule?

Accepted Answer

$$\frac{x^8$}{y$$^{12}$$}$$

Question 4

Divide the monomials: $$\frac{12x^5$y^3$$}{$$4x^2y$$}$.

Accepted Answer

$$3x^3y^2$

Question 5

If $$b is a $$nonzero real number, what is the value of $$b^0$$?

Accepted Answer

$$1$$

Question 6

Simplify $$\frac{2x^4$y^2$$}{$$8x^2y$$}$.

Accepted Answer

$$\frac{1}{4}x^2$y$$

Question 7

Which of the following is the result of dividing $$\frac{15x^3$y^2$$}{$$5x^2y$$}$?

Accepted Answer

$$3x y$$

Question 8

A biologist divides the expression $$\frac{m^6$}{m^2$} to $$model cell growth. What is the simplified form?

Accepted Answer

$$m^4$$

Question 9

Simplify $$\left(\frac{3x}{2y}\$$right)^3$$ using the quotients-to-powers rule.

Accepted Answer

$$\frac{27x^3$}{8y^3$}$$

Question 10

Divide the polynomial $$\frac{6x^3$ + 12x^2$ - 18x}{3x}.$$

Accepted Answer

$$2x^2 + 4x - 6$

Question 11

A chemist divides $$\frac{8a^5$b^2$$}{$$2a^2b$$}$ to calculate the concentration of a solution. What is the simplified result?

Accepted Answer

$$4a^3b$

Question 12

Which of the following is the correct check for the division $$\frac{12x^2$}{3x}$$, if the quotient is $$4x$$?

Accepted Answer

$$3x 	imes 4x = 12x^2$

Question 13

Divide the polynomial $$\frac{9x^4$ - 6x^3$ + 3x^2$}{3x^2$}.$$

Accepted Answer

$$3x^2 - 2x + 1$

Question 14

Simplify $$\left(\frac{2a^2$}{b}\$$right)^2$$ using the quotients-to-powers rule.

Accepted Answer

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

Question 15

A medical researcher divides $$\frac{20x^3$y^2$$}{$$5x^2y$$}$ to analyze gene expression. What is the simplified form?

Accepted Answer

$$4x y$$

Question 16

Which of the following is the result of $$\frac{7x^0$y^3$$}{$$y^3$$}$?

Accepted Answer

$$7$$

Question 17

Divide the polynomial $$\frac{8x^3$ + 4x^2$ - 12x}{4x}.$$

Accepted Answer

$$2x^2 + x - 3$

Question 18

Simplify $$\frac{10x^0$y^2$$}{$$2y^2$$}$.

Accepted Answer

$$5$$

Question 19

Which of the following is the result of $$\left(\frac{a^3$b}{2c^2$}\$$right)^2$$?

Accepted Answer

$$\frac{a^6$b^2$$}{$$4c^4$$}$

Question 20

A physicist divides $$\frac{18x^2$y^4$$}{6x $$y^2$$}$ to calculate energy distribution. What is the simplified result?

Accepted Answer

$$3x y^2$

Dividing Polynomials: Exponent Rules and Polynomial Division

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