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 $\dfrac{2x^7y^3}{4x^2y^5}$ using the quotient rule?

Accepted Answer

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

Question 3

Simplify the following using the power rule: $(a^4b^3)^2$

Accepted Answer

$a^8b^6$

Question 4

Given $\dfrac{7x^7y^4}{2x^3y^2}$, which of the following is the correct simplification?

Accepted Answer

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

Question 5

Evaluate $3^4 	imes 2^3$ without a calculator.

Accepted Answer

$216$

Question 6

Which of the following is the correct scientific notation for $0.0000078$?

Accepted Answer

$7.8 	imes 10^{-6}$

Question 7

Multiply and write the answer in scientific notation: $(2.7 	imes 10^4) 	imes (3.8 	imes 10^7)$

Accepted Answer

$1.026 	imes 10^{11}$

Question 8

Avogadro's number is approximately $602,214,199,000,000,000,000,000$. Which of the following is Avogadro's number in scientific notation?

Accepted Answer

$6.02214199 	imes 10^{23}$

Question 9

A square has a side length of $2.56$ cm. What is its area, rounded to two decimal places?

Accepted Answer

$6.55$ cm$^2$

Question 10

Given the formula $A = P\left(1 + \dfrac{r}{n}\right)^{nt}$, which variable represents the number of times interest is compounded per year?

Accepted Answer

$n$

Question 11

Simplify the following expression with positive exponents: $\dfrac{18x^{-7}y^3}{2x^{-3}y^{-2}}$

Accepted Answer

$9x^{-4}y^5$

Question 12

Write $5,857,000$ in scientific notation.

Accepted Answer

$5.857 	imes 10^6$

Question 13

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

Accepted Answer

$250,000,000$

Question 14

A triangle has a base of $2.48$ cm and a height of $3.6$ cm. What is its area, rounded to two decimal places?

Accepted Answer

$4.46$ cm$^2$

Question 15

What is the degree of the polynomial $5a^4b^2 - 12a^2b^4 + 45$?

Accepted Answer

$6$

Question 16

Which of the following is the correct simplified form of $x^4 \cdot x^7$?

Accepted Answer

$x^{11}$

Question 17

Divide $x^8$ by $x^3$ and simplify.

Accepted Answer

$x^5$

Question 18

If $A = s^2$ and $s = 5.12$ cm, what is the area of the square?

Accepted Answer

$26.21$ cm$^2$

Question 19

Which of the following is the correct simplified form of $a^3b^4 \cdot a^2b^5$?

Accepted Answer

$a^5b^9$

Question 20

Given the formula $A = P\left(1 + \dfrac{r}{n}\right)^{nt}$, what is the value of $A$ if $P = 5000$, $r = 0.04$, $n = 12$, and $t = 5$? (Round to the nearest cent)

Accepted Answer

$6,083.71$

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

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