Question 1

Which of the following correctly applies the power rule to simplify $\left( x^3 \right)^4$?

Accepted Answer

$x^{12}$

Question 2

Simplify the expression $\dfrac{5^7}{5^3}$ using the properties of exponents.

Accepted Answer

$5^4$

Question 3

Which of the following is equivalent to $\dfrac{a^{-3}b^2}{a^2b^{-4}}$ with positive exponents?

Accepted Answer

$\dfrac{b^6}{a^5}$

Question 4

If $x^{-2} = 16$, what is the value of $x$?

Accepted Answer

$\dfrac{1}{4}$

Question 5

Which property of exponents justifies the step $b^m \cdot b^n = b^{m+n}$?

Accepted Answer

Product Rule

Question 6

Simplify $\left( \dfrac{2x^3}{y^2} \right)^2$.

Accepted Answer

$\dfrac{4x^6}{y^4}$

Question 7

Which of the following is equivalent to $\sqrt[3]{x^6}$?

Accepted Answer

$x^2$

Question 8

A biologist is studying bacteria growth modeled by $N = 2^t$, where $t$ is time in hours. If the population after 3 hours is $N = 2^3$, what is the population?

Accepted Answer

$8$

Question 9

Simplify $\dfrac{(3x^2y^{-1})^3}{9x^3y^{-2}}$ and write your answer with positive exponents.

Accepted Answer

$x^3y^3$

Question 10

Which of the following is the correct application of the zero exponent rule?

Accepted Answer

$a^0 = 1$ for any $a 
eq 0$

Question 11

Simplify $\left( \dfrac{a^2b^{-3}}{a^{-1}b^2} \right)^2$.

Accepted Answer

$a^6b^{-10}$

Question 12

Which of the following is equivalent to $\dfrac{1}{x^{-5}}$?

Accepted Answer

$x^5$

Question 13

A chemist dilutes a solution so that its concentration halves every hour. If the initial concentration is $C_0$, which expression gives the concentration after $t$ hours?

Accepted Answer

$C_0 \cdot (\dfrac{1}{2})^t$

Question 14

Simplify $\left( x^{-2}y^3 \right)^2$ and write your answer with positive exponents.

Accepted Answer

$\dfrac{y^6}{x^4}$

Question 15

Which of the following is equivalent to $\sqrt[4]{x^8}$?

Accepted Answer

$x^2$

Question 16

If $a^x = a^y$ and $a 
eq 0$, what must be true?

Accepted Answer

$x = y$

Question 17

Simplify $\dfrac{(2x^{-1}y^2)^3}{4x^2y^{-1}}$ and write your answer with positive exponents.

Question 18

Which of the following is the correct application of the negative exponent rule?

Accepted Answer

$a^{-n} = \dfrac{1}{a^n}$

Question 19

Simplify $\left( \dfrac{3x^2}{y^3} \right)^2$.

Accepted Answer

$\dfrac{9x^4}{y^6}$

C1

Study Guide - Practice Questions

Study Guide - Flashcards