Q: Evaluate the expression $$3 + [4 \times 2 - (5 + 3)]$$ using the correct order of operations.

$$3 + [4 \times 2 - (5 + 3)] = 3 + [8 - 8] = 3 + 0 = 3$$

Q: Which of the following is the correct application of the order of operations for $$6 - 2 \times (3 + 1)^2$?

$$6 - 2 \times (3 + 1)^2$ = 6 - 2 \times 16 = 6 - 32 = -26$$

Q: If $$a = 2$$ and $$b = -3$$, what is the value of $$3a^2b$?

$$3a^2b = 3$$ \times $$(2)^2$$ \times (-3) = 3 \times 4 \times (-3) = -36$$

Question 1

Evaluate the expression $$3 + [4 	imes 2 - (5 + 3)]$$ using the correct order of operations.

Accepted Answer

$$3 + [4 	imes 2 - (5 + 3)] = 3 + [8 - 8] = 3 + 0 = 3$$

Question 2

If $$x = -2$$ and $$y = 5$$, what is the value of $$2x + 3y$$?

Accepted Answer

$$2x + 3y = 2(-2) + 3(5) = -4 + 15 = 11$$

Question 3

Which of the following is the correct domain for the variable $$x in $$the expression $$\frac{5}{x-4}$$?

Accepted Answer

$$x 
eq 4$$

Question 4

Simplify the expression $$\frac{2}{3} + \frac{5}{6} by $$finding a common denominator.

Accepted Answer

$$\frac{2}{3} + \frac{5}{6} = \frac{4}{6} + \frac{5}{6} = \frac{9}{6} = \frac{3}{2}$$

Question 5

What is the least common multiple (LCM) of 12 and 18?

Accepted Answer

36

Question 6

Using the laws of exponents, simplify $$x^3$$ \cdot $$x^5.$$

Accepted Answer

$$x^8$$

Question 7

Rewrite the expression $$\frac{a$$^{-2}$$b^3$$}{$$b^{-1}a$$}$ with only positive exponents.

Accepted Answer

$$\frac{b^4$}{a^3$}$$

Question 8

Evaluate the principal square root: $$\sqrt{49}.$$

Accepted Answer

7

Question 9

Which of the following is equivalent to $$\left(\frac{2}{5}\$$right)^{-3}$$?

Accepted Answer

$$\frac{125}{8}$$

Question 10

A chemist needs to add $$\frac{3}{8} L of $$solution A and $$\frac{1}{6} L of $$solution B to a beaker. What is the total volume in the beaker after both are added?

Accepted Answer

$$\frac{13}{24} L$$

Question 11

Simplify the expression $$\frac{2}{3} \div \frac{4}{5}.$$

Accepted Answer

$$\frac{5}{6}$$

Question 12

If $$x = 0$$, what is the value of $$x^0$$?

Accepted Answer

Undefined

Question 13

Which of the following is the correct application of the order of operations for $$6 - 2 	imes (3 + 1)^2$?

Accepted Answer

$$6 - 2 	imes (3 + 1)^2$ = 6 - 2 	imes 16 = 6 - 32 = -26$$

Question 14

A medical researcher is analyzing a formula $$\sqrt{x^2$}$$ for a measurement $$x. If$$ $$x = -12$$, what is the value of $$\sqrt{x^2$}$$?

Accepted Answer

12

Question 15

Which of the following is the correct simplification of $$\$$left(3^2$$\$$right)^3$$?

Accepted Answer

$$3^6 = 729$

Question 16

A recipe calls for $$\frac{2}{5}$$ cup of sugar and $$\frac{1}{4}$$ cup of honey. What is the total amount of sweetener needed, expressed as a single fraction in simplest form?

Accepted Answer

$$\frac{13}{20}$$

Question 17

Which of the following is the correct result of $$\frac{7}{12} - \frac{1}{8}$$?

Accepted Answer

$$\frac{11}{24}$$

Question 18

If $$a = 2$$ and $$b = -3$$, what is the value of $$3a^2b$?

Accepted Answer

$$3a^2b = 3$$ 	imes $$(2)^2$$ 	imes (-3) = 3 	imes 4 	imes (-3) = -36$$

Question 19

Which of the following is the correct simplification of $$\frac{5}{x-2}$$? What is the domain of $$x$$?

Accepted Answer

The expression is defined for all real $$x$$ except $$x = 2$$

Question 20

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

Accepted Answer

$$P_0$$ \cdot 2^n$$

Real Numbers and Algebra Essentials: Precalculus Study Notes

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