Question 1

Which of the following correctly applies the Power of a Product Rule to the expression $ (2x^3)^4 $?

Accepted Answer

$2^4 x^{12}$

Question 2

A chemist is diluting a solution and models the concentration as $C = 5 	imes 10^{-3}$ mol/L. If the concentration is halved three times, what is the new concentration?

Accepted Answer

$6.25 	imes 10^{-4}$ mol/L

Question 3

Which of the following is the correct application of the Zero Exponent Rule?

Accepted Answer

$(-7)^0 = 1$

Question 4

A medical dosage formula is given by $D = \frac{a^5}{a^2}$. Simplify the expression for $D$ using the Power of a Quotient Rule.

Accepted Answer

$a^3$

Question 5

Which of the following equations is a linear equation in one variable?

Accepted Answer

$7 - 4x = 4x$

Question 6

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

Accepted Answer

$P_0 \cdot 2^n$

Question 7

Simplify the expression $3x + 2x - (3x + 2x)$ using the properties of equality and combining like terms.

Accepted Answer

$0$

Question 8

Which property of equality justifies the following step in solving an equation: $x + 5 = 12 \implies x = 12 - 5$?

Accepted Answer

Subtraction Property of Equality

Question 9

Solve for $x$: $0.2x + 0.4 = 1.2$

Accepted Answer

$x = 4$

Question 10

A recipe calls for $\frac{2}{3}$ cup of sugar and $\frac{1}{4}$ cup of oil. What is the least common denominator (LCD) for these fractions?

Accepted Answer

$12$

Question 11

Which of the following correctly applies the Product Rule for Exponents to $x^2 \cdot x^5$?

Accepted Answer

$x^7$

Question 12

A physics formula is given as $F = ma$. If $m = 3^2$ kg and $a = 2^3$ m/s$^2$, what is $F$?

Accepted Answer

$72$ N

Question 13

Which of the following is NOT a linear equation?

Accepted Answer

$x^2 + x = 6$

Question 14

If $a = 2$ and $b = 3$, what is the value of $(ab)^2$ according to the Power of a Product Rule?

Accepted Answer

$36$

Question 15

A car rental company charges a base fee of $b$ dollars plus $m$ dollars per mile. Which equation models the total cost $C$ for $x$ miles driven?

Accepted Answer

$C = b + mx$

Question 16

Which of the following demonstrates the correct use of the Quotient Rule for Exponents?

Accepted Answer

$\frac{x^7}{x^3} = x^4$

Question 17

Solve for $x$ in the equation $\frac{3}{5}x = 9$ using the multiplication property of equality.

Accepted Answer

$x = 15$

Question 18

A scientist records the temperature drop as $T = 20 - 3x$, where $x$ is the number of hours. What is the temperature after 4 hours?

Accepted Answer

$8$

Question 19

Which of the following is the correct simplification of $\left( x^2 \right)^3$ using the Power Rule for Exponents?

Accepted Answer

$x^6$

Question 20

A student solves the equation $2x + 3 = 11$ by subtracting 3 from both sides and then dividing by 2. What property of equality is used in the second step?

Accepted Answer

Multiplication Property of Equality

Fundamental Properties and Techniques in Precalculus Algebra

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