$$6.02214199 \times 10$$^{23}$$

$$\dfrac{1}{2} \times \text{base} \times \text{height}$$

Question 1

Simplify the following expression using the product rule: $$k(-3a^2b^3$)(15a^4b^2$)$

Accepted Answer

$$-45a^6b^5$

Question 2

Which of the following correctly applies the quotient rule to $$\dfrac{2x^7$y^5$$}{$$8x^3y^2$}$$?

Accepted Answer

$$\dfrac{x^4$y^3$$}{4}$

Question 3

Simplify the following using the power rule: $$(a^4b^3$)^2$$

Accepted Answer

$$a^8b^6$

Question 4

A chemist is working with Avogadro's number, which is approximately $$602,214,199,000,000,000,000,000. $$What is this number in scientific notation?

Accepted Answer

$$6.02214199 	imes 10$$^{23}$$

Question 5

Multiply and write the answer in scientific notation: $$(7.8 	imes 10^7$) 	imes (3.6 	imes 10^4$)$$

Accepted Answer

$$2.808 	imes 10$$^{12}$$

Question 6

Evaluate $$x^3$$ when $$x = 2$$ without using a calculator.

Accepted Answer

$$8$$

Question 7

Which of the following is the correct formula for the area of a triangle?

Accepted Answer

$$\dfrac{1}{2} 	imes 	ext{base} 	imes 	ext{height}$$

Question 8

Given the formula $$A = P \left(1 + \dfrac{r}{n}\$$right)^{nt}$$, which variable represents the principal (initial amount)?

Accepted Answer

$$P$$

Question 9

Simplify the following expression with positive exponents: $$\dfrac{18x^7$y^5$$}{$$3x^2y^2$}$$

Accepted Answer

$$6x^5y^3$

Question 10

Write $$0.0000078 in $$scientific notation.

Accepted Answer

$$7.8 	imes 10$$^{-6}$$

Question 11

A student is asked to divide $$x^8 by$$ $$x^3. $$What is the result?

Accepted Answer

$$x^5$$

Question 12

Which of the following is the correct simplified form of $$k^2$$ \cdot $$k^7$$?

Accepted Answer

$$k^9$$

Question 13

A square has a side length of $$2.56 cm. $$What is its area, rounded to two decimal places?

Accepted Answer

$$6.55 cm$^2$$

Question 14

Which of the following is the degree of the polynomial $$5a^4$$ - $$6b^3$$ + $$10a^2b^2$ - 16a^3$ - 5$?

Accepted Answer

$$4$$

Question 15

Given the polynomial $$7a^4$$ - $$2a^2 + 5$, how many terms does it have?

Accepted Answer

$$3$$

Question 16

Which of the following is the correct scientific notation for $$50,500,000$$?

Accepted Answer

$$5.05 	imes 10^7$

Question 17

A triangle has a base of $$2.48 cm $$and a height of $$3.6 cm. $$What is its area, rounded to two decimal places?

Accepted Answer

$$4.46 cm$^2$$

Question 18

Which of the following is the correct simplified form of $$a^4b^3$ \cdot a^2$b^5$$?

Accepted Answer

$$a^6b^8$

Question 19

Divide $$x^7 by$$ $$x^4$$ and simplify.

Accepted Answer

$$x^3$$

Question 20

Which of the following is the correct simplified form of $$x^2y^3$ \cdot x^4$y^2$$?

Accepted Answer

$$x^6y^5$

College Algebra Practice Problems and Solutions: Exponents, Polynomials, and Scientific Notation

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