Question 1

Which of the following numbers is an example of an irrational number?

Accepted Answer

$$\sqrt{2}$$

Question 2

Simplify the following expression using the order of operations: $$2 + 3 	imes (4 - 2)^2$

Accepted Answer

$$20$$

Question 3

Which property of exponents is illustrated by $$\left(a^m\right)^n = a$$^{mn}$$?

Accepted Answer

Power of a Power Property

Question 4

Evaluate $$\sqrt{100 	imes 36}.$$

Accepted Answer

$$60$$

Question 5

Which of the following is NOT a real number?

Accepted Answer

$$\sqrt{-9}$$

Question 6

Simplify the radical $$\sqrt{72}.$$

Accepted Answer

$$6\sqrt{2}$$

Question 7

A chemist needs to dilute a solution by adding water. If the concentration is reduced by a factor of $$\frac{2}{3}$$, what is the new concentration if the original was $$9$$ mol/L?

Accepted Answer

$$6$$ mol/L

Question 8

Evaluate $$(-2)^3 + 4(-5) - 7$.

Accepted Answer

$$-31$$

Question 9

Which of the following is the correct simplification of $$\frac{12x^7$}{4x^2$}$$?

Accepted Answer

$$3x^5$$

Question 10

If $$x = -3$$, evaluate $$|2x - 5|.$$

Accepted Answer

$$11$$

Question 11

Simplify $$\left(\frac{3x^2$}{5x}\$$right)^2$$.

Accepted Answer

$$\frac{9}{25x^2$}$$

Question 12

A biologist measures the area of a petri dish as $$\pi r^2$ where r = 4$ cm. What is the area?

Accepted Answer

$$16\pi cm$^2$$

Question 13

Which of the following is the result of $$\sqrt[3]{-27}$$?

Accepted Answer

$$-3$$

Question 14

Simplify the expression $$(x^3 + 4x$$)$$.

Accepted Answer

$$x^3 + 4x$

Question 15

A medical researcher calculates the dosage of a drug using the formula $$d = \frac{mg}{kg}. If a $$patient weighs $$70 kg $$and the dosage is $$2 mg/kg$$, what is the total dosage?

Accepted Answer

$$140 mg$$

Question 16

Which of the following is the correct simplification of $$\frac{5}{4} 	imes \frac{3}{5}$$?

Accepted Answer

$$\frac{3}{4}$$

Question 17

Evaluate $$(-6)^4.$$

Accepted Answer

$$1296$$

Question 18

Simplify $$4^5$$ 	imes $$4^2$$ using properties of exponents.

Accepted Answer

$$4^7$$

Question 19

Which of the following is the correct simplification of $$\sqrt{63}$$?

Accepted Answer

$$3\sqrt{7}$$

Question 20

A student calculates $$\frac{2.7 - 9.4}{9 - 7}$$ for a chemistry experiment. What is the result?

Accepted Answer

College Algebra Review: Numbers, Operations, Exponents, Radicals, and Polynomials

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