Question 1

Which of the following correctly applies the product rule to simplify the expression $2x^3y^2 \cdot 5x^4y^5$?

Accepted Answer

$10x^7y^7$

Question 2

A biologist is studying bacteria growth. The population doubles every hour. If the initial population is $P_0$, which expression represents the population after $n$ hours?

Accepted Answer

$P_0 \cdot 2^n$

Question 3

Simplify the following expression using the quotient rule: $\dfrac{18x^7y^5}{6x^3y^2}$

Accepted Answer

$3x^4y^3$

Question 4

Which of the following is equivalent to $a^{-4}b^2$ using only positive exponents?

Accepted Answer

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

Question 5

A chemist measures a sample with a mass of $0.0000452$ grams. What is this mass in scientific notation?

Accepted Answer

$4.52 	imes 10^{-5}$

Question 6

Simplify the expression $\left(2x^2y^3\right)^4$ using the appropriate exponent rules.

Accepted Answer

$16x^8y^{12}$

Question 7

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

Accepted Answer

$(-7x^5y^2)^0 = 1$

Question 8

A medical laboratory reports a virus concentration as $3.2 	imes 10^6$ particles per milliliter. What is this number in standard decimal notation?

Accepted Answer

$3,200,000$

Question 9

Simplify the following expression using the power rule: $\left(x^3y^2\right)^5$

Accepted Answer

$x^{15}y^{10}$

Question 10

Which of the following expressions is equivalent to $\dfrac{(2x^3y^2)^2}{4x^2y^5}$?

Accepted Answer

$x^4y^{-1}$

Question 11

A city’s population is $1.25 	imes 10^7$. Which of the following is the correct way to write this number in decimal notation?

Accepted Answer

$12,500,000$

Question 12

Simplify the following expression and write your answer with only positive exponents: $\dfrac{3x^{-2}y^4}{6x^3y^{-1}}$

Accepted Answer

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

Question 13

Which of the following is the correct simplification of $\left(\dfrac{a^2b^3}{c^4}\right)^3$?

Accepted Answer

$\dfrac{a^6b^9}{c^{12}}$

Question 14

A scientist records a measurement as $7.89 	imes 10^{-4}$ meters. Which of the following is the correct decimal representation?

Accepted Answer

$0.000789$

Question 15

Which of the following is the correct simplification of $\dfrac{5x^7y^2}{10x^3y^5}$?

Accepted Answer

$\dfrac{x^4}{2y^3}$

Question 16

Simplify the following expression: $\left(-3x^2y\right)^3$

Accepted Answer

$-27x^6y^3$

Question 17

Which of the following is the correct application of the negative exponent rule to $\dfrac{1}{x^{-3}}$?

Accepted Answer

$x^3$

Question 18

A pharmaceutical company produces $2.5 	imes 10^8$ tablets per year. How many tablets is this in standard decimal notation?

Accepted Answer

$250,000,000$

Question 19

Simplify the following expression: $\dfrac{(3x^2y^{-3})^2}{x^{-4}y}$

Accepted Answer

$9x^8y^{-7}$

Exponents and Scientific Notation: Fundamental Concepts in College Algebra

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