Q: Avogadro's number is approximately $$602,214,199,000,000,000,000,000. $$Which of the following is Avogadro's number in scientific notation?

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

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 is the correct simplification of $$\dfrac{2x^7$y^3$$}{$$4x^2y^5$}$$ using the quotient rule?

Accepted Answer

$$\dfrac{x^5$}{2y^2$}$$

Question 3

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

Accepted Answer

$$a^8b^6$

Question 4

Given $$\dfrac{7x^7$y^4$$}{$$2x^3y^2$}$$, which of the following is the correct simplification?

Accepted Answer

$$\dfrac{7x^4$y^2$$}{2}$

Question 5

Evaluate $$3^4$$ 	imes $$2^3$$ without a calculator.

Accepted Answer

$$216$$

Question 6

Which of the following is the correct scientific notation for $$0.0000078$$?

Accepted Answer

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

Question 7

Multiply and write the answer in scientific notation: $$(2.7 	imes 10^4$) 	imes (3.8 	imes 10^7$)$$

Accepted Answer

$$1.026 	imes 10$$^{11}$$

Question 8

Avogadro's number is approximately $$602,214,199,000,000,000,000,000. $$Which of the following is Avogadro's number in scientific notation?

Accepted Answer

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

Question 9

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 10

Given the formula $$A = P\left(1 + \dfrac{r}{n}\$$right)^{nt}$$, which variable represents the number of times interest is compounded per year?

Accepted Answer

$$n$$

Question 11

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

Accepted Answer

$$9x^{-4}y^5$

Question 12

Write $$5,857,000 in $$scientific notation.

Accepted Answer

$$5.857 	imes 10^6$

Question 13

Which of the following is the correct standard form of $$2.5 	imes 10^8$?

Accepted Answer

$$250,000,000$$

Question 14

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 15

What is the degree of the polynomial $$5a^4b^2$ - 12a^2$b^4 + 45$?

Accepted Answer

$$6$$

Question 16

Which of the following is the correct simplified form of $$x^4$$ \cdot $$x^7$$?

Accepted Answer

$$x^{11}$$

Question 17

Divide $$x^8 by$$ $$x^3$$ and simplify.

Accepted Answer

$$x^5$$

Question 18

If $$A = s^2$ and s = 5.12$ cm, what is the area of the square?

Accepted Answer

$$26.21 cm$^2$$

Question 19

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

Accepted Answer

$$a^5b^9$

Question 20

Given the formula $$A = P\left(1 + \dfrac{r}{n}\$$right)^{nt}$$, what is the value of A$ if P = 5000$, r = 0.04$, n = 12$, and t = 5$? (Round to the nearest cent)

Accepted Answer

$$6,083.71$$

College Algebra: Exponents, Polynomials, and Scientific Notation Study Guide

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