Question 1

Which of the following correctly applies the product rule for exponents to simplify $$x^5$$ \cdot $$x^7$$?

Accepted Answer

$$x^{12}$$

Question 2

A biologist is tracking the growth of bacteria, which doubles every hour. If the initial population is $$y$$, what is the population after 3 hours, expressed in exponential form?

Accepted Answer

$$y \cdot 2^3$

Question 3

Simplify $$\left(3y\$$right)^4$$ using the products to powers rule.

Accepted Answer

$$81y^4$$

Question 4

A chemist mixes two solutions, each containing $$z^2$$ and $$z^6$$ molecules of a compound. What is the total number of molecules after mixing, using the product rule for exponents?

Accepted Answer

$$z^8$$

Question 5

Simplify $$\left(5x\$$right)^3$$ using the products to powers rule.

Accepted Answer

$$125x^3$$

Question 6

Multiply the monomials $$10x^2$$ and $$7x^4.$$

Accepted Answer

$$70x^6$$

Question 7

A pharmaceutical company produces $$4x^2$$ units of a drug each day. If production increases to $$3x^3$$ units per day, what is the combined production after one day, using the product rule?

Accepted Answer

$$12x^5$$

Question 8

Multiply the monomial $$-10x^6 by$$ $$5x^{10}.$$

Accepted Answer

$$-50x^{16}$$

Question 9

Simplify $$\$$left(2x^3$$\$$right)^4$$ using the products to powers rule.

Accepted Answer

$$16x^{12}$$

Question 10

Multiply the monomial $$4x^2 by $$the polynomial $$x + 2.$$

Accepted Answer

$$4x^3$$ + $$8x^2$$

Question 11

A company’s revenue is modeled by $$3x^2 + 4x + 5$. If the company triples its output, what is the new revenue expression?

Accepted Answer

$$9x^2 + 12x + 15$

Question 12

Multiply the binomials $$(x + 3)(x + 2)$$ using the FOIL method.

Accepted Answer

$$x^2 + 5x + 6$

Question 13

Multiply the binomials $$(x + 7)(x - 4).$$

Accepted Answer

$$x^2 + 3x - 28$

Question 14

Multiply the binomials $$(y + 4)(y - 2).$$

Accepted Answer

$$y^2 + 2y - 8$

Question 15

A physics formula involves multiplying $$(x + 5) by$$ $$(x + 2). $$What is the expanded form?

Accepted Answer

$$x^2 + 7x + 10$

Question 16

Simplify $$\left(3y\$$right)^2$$ \cdot \$$left(2y^3$$\right)$$ using exponent rules.

Accepted Answer

$$18y^5$$

Question 17

Multiply the binomials $$(x + 2)(x + 4)$$ and select the correct expanded form.

Accepted Answer

$$x^2 + 6x + 8$

Question 18

A medical researcher models the spread of a virus with $$y^2 + 3y$. If the number of cases triples, what is the new expression?

Accepted Answer

$$3y^2 + 9y$

Question 19

Simplify $$\$$left(2x^2$$y\$$right)^3$$ using exponent rules.

Accepted Answer

$$8x^6y^3$

Question 20

Multiply the binomials $$(x - 3)(x + 5)$$ and select the correct expanded form.

Accepted Answer

$$x^2 + 2x - 15$

Multiplying Polynomials and Exponent Rules (Section R3.2)

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