Question 1

Evaluate the expression $$-4^2.$$

Accepted Answer

$$-16$$

Question 2

Simplify the expression $$m^6$$ \cdot $$m^5$$ \cdot $$m^9$$ using the product rule for exponents.

Accepted Answer

$$m^{20}$$

Question 3

Simplify $$(-6p^3)(3p^5$)$.

Accepted Answer

$$-18p^8$$

Question 4

Use the power rule to simplify $$(4a)^3.$$

Accepted Answer

$$64a^3$$

Question 5

Simplify $$(x^6y)^3$ using the power of a product rule.

Accepted Answer

$$x^{18}y^3$

Question 6

Simplify the expression $$\dfrac{a^9$}{a}$$ using the quotient rule.

Accepted Answer

$$a^8$$

Question 7

Simplify $$-8y^0.$$

Accepted Answer

$$-8$$

Question 8

Write $$290,000 in $$scientific notation.

Accepted Answer

$$2.9 	imes 10^5$

Question 9

Write $$0.000372 in $$scientific notation.

Accepted Answer

$$3.72 	imes 10$$^{-4}$$

Question 10

Write $$7.6024 	imes 10^4$ in standard notation.

Accepted Answer

$$76,024$$

Question 11

Evaluate the polynomial $$3x^2 - 2x - 4$ when x = -1$.

Accepted Answer

$$1$$

Question 12

Combine like terms: $$9x^7$$ + $$7x^7$$ - $$4x^7.$$

Accepted Answer

$$12x^7$$

Question 13

Add the polynomials: $$(8x^2 - 3x - 6$$) + $$(3x^2 - 3x - 6$$)$$.

Accepted Answer

$$11x^2 - 6x - 12$

Question 14

Subtract the polynomials: $$(2x^7$$ + $$15x^4 - 3$$) - $$(8x^7$$ + $$9x^4 - 17$$)$$.

Accepted Answer

$$-6x^7$$ + $$6x^4 + 14$

Question 15

Multiply: $$-3x^7(-9x^6$ + 7x^2$ + 4)$.

Accepted Answer

$$27x^{13}$$ - $$21x^9$$ - $$12x^7$$

Question 16

Multiply using the FOIL method: $$(x + 5)(x + 2).$$

Accepted Answer

$$x^2 + 7x + 10$

Question 17

Expand $$(n + 15)^2$.

Accepted Answer

$$n^2 + 30n + 225$

Question 18

Divide: $$\dfrac{-12x^9$ - 24x^6$}{-4x^3$}.$$

Accepted Answer

$$3x^6$$ + $$6x^3$$

Question 19

Divide: $$\dfrac{x^2$ + 12x + 35}{x + 5}.$$

Accepted Answer

$$x + 7$$

Question 20

A biologist is studying the growth of a bacteria culture. The number of bacteria triples every hour. If the initial population is $$P_0$$, which expression represents the population after $$n$$ hours?

Accepted Answer

$$P_0$$ \cdot 3^n$$

Preparatory Algebra Chapter 3 Test – Step-by-Step Study Guidance

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