Question 1

Simplify the expression $$6^2$$ \cdot $$6^3$$ and choose the correct answer.

Accepted Answer

$$6^5$$

Question 2

Which of the following is the simplified form of $$9x^2$$ \cdot $$3x^2$$?

Accepted Answer

$$27x^4$$

Question 3

If $$y^8$$ \div $$y^3 is $$simplified, what is the result?

Accepted Answer

$$y^5$$

Question 4

Simplify $$\frac{a^7$b^5$$}{$$a^2b^3$}.$$

Accepted Answer

$$a^5b^2$

Question 5

Which of the following is equivalent to $$(2x^3y^2$)^2$$?

Accepted Answer

$$4x^6y^4$

Question 6

Simplify $$\frac{10x^7$}{2x^3$}.$$

Accepted Answer

$$5x^4$$

Question 7

What is the simplified form of $$(5a^2b^3$)^2$$?

Accepted Answer

$$25a^4b^6$

Question 8

If $$x^3y^4$ \cdot x^2$y$ is simplified, what is the result?

Accepted Answer

$$x^5y^5$

Question 9

Simplify $$\frac{8x^5$y^3$$}{$$2x^2y$$}$.

Accepted Answer

$$4x^3y^2$

Question 10

Which of the following is the correct simplification of $$(6a^2b^3$c^2$$)^{-2}$?

Accepted Answer

$$\frac{1}{36a^4$b^6c^4$}$$

Question 11

A scientist is diluting a solution and the concentration is modeled by $$C = 100x$$^{-2}$$. If x$ is doubled, what happens to the concentration?

Accepted Answer

It becomes one-fourth as much.

Question 12

Simplify $$\frac{a^2$b^5$$}{$$a^5b^2$}.$$

Accepted Answer

$$\frac{b^3$}{a^3$}$$

Question 13

Which of the following is the simplified form of $$\frac{3x^2$y^5$$}{$$9x^5y^2$}$$?

Accepted Answer

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

Question 14

If $$y = 8x$$^{-2}$$, what is y$ when x = 2$?

Accepted Answer

$$2$$

Question 15

Simplify $$(2a^2b$$^{-3}$$)^2.$$

Accepted Answer

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

Question 16

Which of the following is the simplified form of $$\frac{2x$$^{-3}$$y^4$$}{$$4x^2y$$^{-2}$$}$$?

Accepted Answer

$$\frac{y^6$}{2x^5$}$$

Question 17

A medication's effectiveness is modeled by $$E = 50t$$^{-1}$$, where t$ is time in hours. What is the effectiveness after 5 hours?

Accepted Answer

$$10$$

Question 18

Simplify $$\frac{(3x^2$y^3)^2$}{9x^3$y}.$$

Accepted Answer

$$x y^5$

Question 19

Which of the following is the simplified form of $$\frac{a^2$b^{-3}$$}{$$a^{-1}b^2$}$$?

Accepted Answer

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

Question 20

Simplify $$(2x^{-2}y^3$)^3.$$

Accepted Answer

$$8x^{-6}y^9$

College Algebra Study Guide: Multiplying, Dividing, and Simplifying Exponents

Study Guide - Practice Questions