Q: Avogadro's number is approximately $$602,214,199,000,000,000,000,000. $$Write 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 $$\dfrac{2x^7$y^5$$}{$$4x^3y^2$}$$ using the quotient rule?

Accepted Answer

$$\dfrac{x^4$y^3$$}{2}$

Question 3

Simplify the following using the power of a power rule: $$(a^4)^5$

Accepted Answer

$$a^{20}$$

Question 4

Given $$k = 2x^3$y^2$$, what is $$k^2$?

Accepted Answer

$$4x^6y^4$

Question 5

Evaluate $$\dfrac{7x^7$y^4$$}{$$2x^3y^2$}$$ using the quotient rule.

Accepted Answer

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

Question 6

Simplify $$6a^4b^2$ \cdot 8a^2$b^3$$ using the product rule.

Accepted Answer

$$48a^6b^5$

Question 7

Which of the following is the correct scientific notation for 0.000029?

Accepted Answer

$$2.9 	imes 10$$^{-5}$$

Question 8

Multiply and write the answer in scientific notation: $$(7.16 	imes 10^4$) 	imes (2.3 	imes 10^3$)$$

Accepted Answer

Question 9

Avogadro's number is approximately $$602,214,199,000,000,000,000,000. $$Write Avogadro's number in scientific notation.

Accepted Answer

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

Question 10

A formula for compound interest is $$A = P \left(1 + \dfrac{r}{n}\$$right)^{nt}$$. If you invest P = 5000$ at r = 0.04$ compounded monthly for t = 5$ years, what is the value of A$? (Round to the nearest cent)

Accepted Answer

$$6,083.60$$

Question 11

Given the polynomial $$-5a^2$$ - $$6b^3$$ + $$10a^2b^2$ - 16a^3$ - 5$, what is its degree?

Accepted Answer

3

Question 12

What is the area of a triangle with base $$2.56 cm $$and height $$3.48 cm$$? (Round to two decimal places)

Accepted Answer

$$4.46 cm$^2$$

Question 13

Simplify $$x^2y^3$ \cdot x^4$y^2$$ using the product rule.

Accepted Answer

$$x^6y^5$

Question 14

Divide $$x^7y^4$ by x^3$y^2$$ and simplify.

Accepted Answer

$$x^4y^2$

Question 15

Write $$50,500,000 in $$scientific notation.

Accepted Answer

$$5.05 	imes 10^7$

Question 16

If the area of a square is $$2.56 cm$^2$$, what is the length of one side? (Round to two decimal places)

Accepted Answer

$$1.60 cm$$

Question 17

Which of the following is the correct simplified form of $$\dfrac{a^8$b^7$$}{$$a^3b^2$}$$?

Accepted Answer

$$a^5b^5$

Question 18

Given the formula for the area of a rectangle $$A = 	ext{length} 	imes 	ext{width}$$, what is the area if the length is $$5.21 m $$and the width is $$4.3 m$$?

Accepted Answer

$$22.40 m$^2$$

Question 19

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

Accepted Answer

$$250,000,000$$

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

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