Plz answer 20points karen has been studying fractions, decimals, and exponents in math class with mrs. hudson. she wanted more practice, so she looked through her science magazines for numbers with exponents. take a look at some of the numbers karen found and see if you can write equivalent values for each of them. remember to use at least two of vocabulary words in the written portion of the assignment. don't forget to review the rubric to see how you will be graded (35 points). 1. apply the properties of integer exponents to write equivalent numerical expressions. show all work. ex. 32 • 3-5 = 3-3 = a. 41 • 42 b. 53 • 5-6 c. 32 • 31 d. 65 • 5-7 e. f. g. h. select two of the above express

A] 4¹×4²
From the laws of integer when you multiply number with the same base, you add their powers. Thus we shall have:
4¹×4²
=4⁽¹⁺²⁾
=4³
=64

64

64

b. 5³×5⁻⁶
since the numbers have the base, we add their powers:
5³×5⁻⁶
=5⁽³⁻⁶⁾
=5⁻³
according to the integer laws
a⁻ᵇ=1/aᵇ
thus our expression will be:
5⁻³
=1/5³
=1/125

1/125

c. 3²×3¹
=3⁽²⁺¹⁾
=3³
=9

9

d.
6⁵×5⁻⁷
=6⁵/5⁷
=7776/78125

7776/78125

e.
8⁵/8³
when you divide numbers with the same base you subtract their powers as follows:
8⁵/8³
=8⁽⁵⁻³⁾
=8²
=64
64

f. 7²/7⁴
As in the above question we shall have:
7²/7⁴
=7⁽²⁻⁴⁾
=7⁻²
=1/7²
=1/49
1/49

g.
 9⁵/9⁷
=9⁽⁵⁻⁷⁾
=9⁻²
=1/9²
=1/81

1/81

h.
5¹/5³
=5⁽¹⁻³⁾
=5⁻²
=1/5²
=1/25

1/25
  

   Select two of the above expressions (one multiplication and one division) and explain how you simplified them.  

a] 4¹×4²
From the laws of integer when you multiply number with the same base, you add their powers. Thus we shall have:
4¹×4²
=4⁽¹⁺²⁾
=4³
=64

b]
8⁵/8³
when you divide numbers with the same base you subtract their powers as follows:
8⁵/8³
=8⁽⁵⁻³⁾
=8²
=64