Algebra quiz

P.2 Integer and Rational Number Exponents Page 1 of 5

SECTION P.2 INTEGER AND RATIONAL NUMBER EXPONENTS

Integer Exponents

Scientific Notation

A number written in scientific notation has the form 𝑎 × 10𝑛, where 1 ≤ 𝑎 < 10 and n is an integer.

Changing a number from its decimal form to scientific notation.

a. For numbers greater than 10, move the decimal point to the right of the first nonzero digit. Exponent n is equal to number of places the decimal point has been moved.

b. For numbers less than 1, move the decimal point to the right of the first nonzero digit. The exponent n will be negative.

P.2 Integer and Rational Number Exponents Page 2 of 5

Changing a number from scientific notation to its decimal form, reverse the procedure.

a. If the exponent is positive, move the decimal point to the right the same number of places as the exponent.

b. If the exponent is negative, move the decimal point to the left the same number of places as the absolute value of the exponent.

Rational Exponents

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Radical Expressions

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Exercise Set P.2

Evaluate each expression.

1. −53 = −(5 ∙ 5 ∙ 5) = −125

7. 5

5

1 2 2.2.2.2.2 32

2    

Write the number in scientific notation.

10. 49,100,000,000 = 4.91 × 10 10

12. 0.000000402 = 4.02 × 10 -7

Change the number from scientific notation to decimal notation.

13. 3.14 × 10 7 = 31400000

16. 6.14 × 10 -8

= 0.0000000614

Evaluate each exponential expression.

18. −163/2 = −(42)3/2 = −43 = −64

22.     4 5 44 5 5

4

1 1 1 32 2 2

2 2.2.2.2 16

      

70. (27𝑥3𝑦6) 2

3 = (33) 2

3(𝑥3) 2

3(𝑦6) 2

3

= 32𝑥6/3𝑦12/3

= 9x 2 y

4

Write the exponential expression in simplest form.

24. 2 3

3 2

4 2 2.2.2 8 1

2 4 4.4 16 2



    

35. (−4𝑥−3𝑦)(7𝑥5𝑦−2) = [−4(7)]𝑥−3+5𝑦1−2 = −28𝑥2𝑦−1 = − 28𝑥2

𝑦

39. 3 4 2

3 5 4 2 2 2

5 2 2

12 2 2 2

18 3 3 3

x y y x y x y

x y x

     

50.  

 

 

 

2 22 3 2 2 3 2 4 6

4 3 6 12 1 6

3 3 3 12 61 3 4 34

3 3 9 9 9 9

8 8 8 822

a b a b a b a a b a b

a b ba ba b

 

  

 

         



Solution 2:

Solution 2:

P.2 Integer and Rational Number Exponents Page 5 of 5

Perform the indicated operation and write the answer in scientific notation.

53. (3 × 1012)(9 × 10−5) = (3 × 9) × 1012−5

= 27 × 107 = 2 ∙ 7 × 101 × 107

= 2.7 × 101+7 = 2.7 × 108

56. 2.5 × 108

5 × 1010 =

2.5

5 × 10

8−10 =

= 0.5 × 10−2 = 5 × 10−1 × 10−2

= 5 × 10−1−2 = 5 × 10−3

Simplify each radical expression and write the result in simplest form.

77. √45 = √9 ∙ 5 = √32 ∙ 5 = 3√5

87. 2 2

2 32 3 98 2 4 2 3 7 2    

2(4) 2 3(7) 2 

8 2 21 2

13 2

 

 

105. 2 2 2 2 2

. 2 22 2 2

  

114.  

 

     2

2

2 5 2 2 5 2 2 5 22 2 5 2 . 2 5 2

5 4 15 2 5 2 5 2 5 2

        

   

Practice Exercises: Solve numbers 5, 9, 15, 19, 25, 33, 45, 49, 51, 55, 78, 97, 106, 113