Question 1

Simplify the following expression using the product rule: $k(-3a^2b^3)(15a^4b^2)$

Accepted Answer

$-45a^6b^5$

Question 2

Which of the following is the correct simplification of $\dfrac{2x^7y^5}{4x^3y^2}$ using the quotient rule?

Accepted Answer

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

Question 3

Simplify the following using the power of a power rule: $(a^4)^5$

Accepted Answer

$a^{20}$

Question 4

Given $k = 2x^3y^2$, what is $k^2$?

Accepted Answer

$4x^6y^4$

Question 5

Evaluate $\dfrac{7x^7y^4}{2x^3y^2}$ using the quotient rule.

Accepted Answer

$\dfrac{7x^4y^2}{2}$

Question 6

Simplify $6a^4b^2 \cdot 8a^2b^3$ using the product rule.

Accepted Answer

$48a^6b^5$

Question 7

Which of the following is the correct scientific notation for 0.000029?

Accepted Answer

$2.9 	imes 10^{-5}$

Question 8

Multiply and write the answer in scientific notation: $(7.16 	imes 10^4) 	imes (2.3 	imes 10^3)$

Question 9

Avogadro's number is approximately $602,214,199,000,000,000,000,000$. Write Avogadro's number in scientific notation.

Accepted Answer

$6.02214199 	imes 10^{23}$

Question 10

A formula for compound interest is $A = P \left(1 + \dfrac{r}{n}\right)^{nt}$. If you invest $P = 5000$ at $r = 0.04$ compounded monthly for $t = 5$ years, what is the value of $A$? (Round to the nearest cent)

Accepted Answer

$6,083.60$

Question 11

Given the polynomial $-5a^2 - 6b^3 + 10a^2b^2 - 16a^3 - 5$, what is its degree?

Accepted Answer

3

Question 12

What is the area of a triangle with base $2.56$ cm and height $3.48$ cm? (Round to two decimal places)

Accepted Answer

$4.46$ cm$^2$

Question 13

Simplify $x^2y^3 \cdot x^4y^2$ using the product rule.

Accepted Answer

$x^6y^5$

Question 14

Divide $x^7y^4$ by $x^3y^2$ and simplify.

Accepted Answer

$x^4y^2$

Question 15

Write $50,500,000$ in scientific notation.

Accepted Answer

$5.05 	imes 10^7$

Question 16

If the area of a square is $2.56$ cm$^2$, what is the length of one side? (Round to two decimal places)

Accepted Answer

$1.60$ cm

Question 17

Which of the following is the correct simplified form of $\dfrac{a^8b^7}{a^3b^2}$?

Accepted Answer

$a^5b^5$

Question 18

Given the formula for the area of a rectangle $A = 	ext{length} 	imes 	ext{width}$, what is the area if the length is $5.21$ m and the width is $4.3$ m?

Accepted Answer

$22.40$ m$^2$

Question 19

Which of the following is the correct standard form for $2.5 	imes 10^8$?

Accepted Answer

$250,000,000$

College Algebra: Exponents, Polynomials, and Scientific Notation Study Guide

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