7-1 Zero and Negative Exponents

Quick Review

You can use zero and negative integers as exponents. For every nonzero number a , a 0 = 1 . eh comma , eh to the , equals 1 .  For every nonzero number a and any integer n, a − n = 1 a n . eh super negative n end super , equals , fraction 1 , over eh to the n end fraction . .  When you evaluate an exponential expression, you can simplify the expression before substituting values for the variables.

Example

What is the value of a 2 b − 4 c 0 eh squared . b super negative 4 end super . c to the  for a = 3 , b = 2 , eh equals 3 comma b equals 2 comma  and c = − 5 ? c equals negative 5 question mark

a 2 b − 4 c 0 = a 2 c 0 b 4 Use the definition of negative exponents .   = a 2 ( 1 ) b 4 Use the definition of zero exponent .   = 3 2 2 4 Substitute .   = 9 16 Simplify . table with 4 rows and 3 columns , row1 column 1 , eh squared . b super negative 4 end super . c to the , column 2 equals . fraction eh squared , c to the , over b to the fourth end fraction , column 3 cap usethedefinitionofnegativeexponents . . , row2 column 1 , , column 2 equals . fraction eh squared . open 1 close , over b to the fourth end fraction , column 3 cap usethedefinitionofzeroexponent . . , row3 column 1 , , column 2 equals . fraction 3 squared , over 2 to the fourth end fraction , column 3 cap substitute . . , row4 column 1 , , column 2 equals , 9 sixteenths , column 3 cap simplify , . , end table

Exercises

Simplify each expression.

6. 5 0 5 to the
7. 7 − 2 7 super negative 2 end super
8. 4 x − 2 y − 8 fraction 4 x super negative 2 end super , over y super negative 8 end super end fraction
9. 1 p 2 q − 4 r 0 fraction 1 , over p squared . q super negative 4 end super . r to the end fraction

Evaluate each expression for x = 2 , y = − 3 , x equals 2 comma y equals negative 3 comma  and z = − 5 . z equals negative 5 .

10. x 0 y 2 x to the , y squared
11. ( − x ) − 4 y 2 open , negative x , close super negative 4 end super . y squared
12. x 0 z 0 x to the , z to the
13. 5 x 0 y − 2 fraction 5 x to the , over y super negative 2 end super end fraction
14. y − 2 z 2 y super negative 2 end super . z squared
15. 2 x y 2 z − 1 fraction 2 x , over y squared . z super negative 1 end super end fraction
16. Reasoning Is it true that ( − 3 b ) 4 = − 12 b 4 ? open negative 3 b close to the fourth . equals negative 12 , b to the fourth , question mark  Explain why or why not.

7-2 Scientific Notation

Quick Review

You can use scientific notation to write very large or very small numbers. A number is written in scientific notation if it has the form a × 10 n , eh times , 10 to the n , comma  where 1 ≤ | a | < 10 1 less than or equal to vertical line eh vertical line less than 10  and n is an integer.

Example

What is each number written in scientific notation?

1. 510,000,000,000

   Move the decimal point 11 places to the left.

2. 0.0000087

   Move the decimal point 6 places to the right.

Exercises

Is the number written in scientific notation? If not, explain why not.

17. 950 × 10 5 950 times , 10 to the fifth
18. 7.23 × 100 8 7.23 , times , 100 to the eighth
19. 1.6 × 10 − 6 1.6 times , 10 super negative 6 end super
20. 0.84 × 10 − 5 0.84 , times , 10 super negative 5 end super

Write each number in scientific notation.

21. 2,793,000
22. 189,000,000
23. 0.000043
24. 0.0000000027
25. 3,860,000,000,000
26. 0.00000478

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