Integer Exponents, Scientific Notation, and Order of ...
Exponent Rules Assignment
Laws of exponents for real numbers a and b and integers m and n:
|Rule |Example |Rule |Example |
|[pic] |[pic] |[pic] |[pic] |
|[pic] |[pic] |[pic] |[pic][pic] |
|[pic] |[pic] |[pic] |[pic] |
|[pic] |[pic] | | |
|[pic] |[pic] |[pic] |[pic] |
Scientific Notation: [pic], where 1 ≤ a < 10 and b is an integer
1. What power do each of the following figures represent? Also evaluate each expression.
(a) (b)
2. Evaluate the following expressions. Show the exponent meaning in your work.
(a) 53 (b) (-3)4 (c) 60 (d) 3 ∙ 52 (e) [pic]
3. True or False. Explain your reasoning. (-2)4 = -24 ___________
Evaluate or simplify using the exponent rules. Show your step-by-step use of the rules!
4. [pic] 5. [pic] 6. [pic] 7. [pic] = 10 = _____ = [pic]
= 10 = 7
= _____
or __________ or 5,764,801
Give a simplified fraction.
8. [pic] 9. [pic] 10. [pic] 11. [pic] = ________ Give a simplified fraction. Give a simplified fraction.
.
Write in scientific notation:
12. $70 billion 13. 0.00016 cm
= $70,000,000,000 = _____ x 10
= _____ x 10
Write in standard decimal number notation.
14. $1.9 × 1013 15. 8.45 × 10-7 seconds
16. Evaluate each expression for the given value of x. Show the substitution and each “order of operation” step toward the solution.
(a) 3x2 ; x = 5 (b) (3x)2 ; x = 4 (c) [pic]
17. Simplify. Use only positive exponents in your answers. Show correct use of the exponent rules.
(a) x6 ∙ x3 ∙ x (b) [pic] (c) [pic]
(d) (-4xy3)2 (e) (a4)-3 (f) [pic]
18. Evaluate.
(a) [pic] (b) [pic]
19. Now, be creative! Make up three problems involving exponents and exponent rules, and show your work toward the solution.
(a)
(b)
(c)
Do your best! Rise to the challenge! Live and learn!
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