Question 1

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

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: $$\dfrac{18x^7$y^5$$}{$$6x^3y^2$}$$

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 $$\$$left(2x^2$$y^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: $$\$$left(x^3$$y^2$$\$$right)^5$

Accepted Answer

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

Question 10

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

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 $$\left(\dfrac{a^2$b^3$$}{$$c^4$$}\$$right)^3$?

Accepted Answer

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

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 $$\dfrac{5x^7$y^2$$}{$$10x^3y^5$}$$?

Accepted Answer

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

Question 16

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

Accepted Answer

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

Exponents and Scientific Notation: Fundamental Concepts in College Algebra

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