Step by Step Solution
Step 1 :
1.1 Negative number raised to an odd power is negative
To show this we begin with (-7)5 ,a negative number raised to an odd exponent:
(-7)5 can be written as (-7)•(-7)•(-7)•(-7)•(-7)
Now, using the rule that says minus times minus is plus, (-7)5 can be written as (49)•(49)•(-7) which is a negative number.
We showed that (-7)5 is a negative number
Using the same arguments as above, replacing (-7) by any negative number, and replacing the exponent 5 by any odd exponent, we proved which had to be proved
1.2 6 = 2•3 (-6)5 = (2•3)5 = -25 • 35
Equation at the end of step 1 :
Step 2 :
2.1 Negative number raised to an even power is positive
For example let's look at (-7)6 , where (-7) , a negative number, is raised to 6 , an even exponent :
(-7)6 can be written as (-7)•(-7)•(-7)•(-7)•(-7)•(-7)
Now, using the rule that says minus times minus is plus, (-7)6 can be written as (49)•(49)•(49) which in turn can be written as (7)•(7)•(7)•(7)•(7)•(7) or 76 which is positive.
We proved that (-7)6 is equal to (7)6 which is a positive number
Using the same arguments as above, replacing (-7) by any negative number, and replacing the exponent 6 by any even exponent, we proved which had to be proved
2.2 6 = 2•3 (-6)8 = (2•3)8 = 28 • 38
Equation at the end of step 2 :
Step 3 :
(28•38)
Simplify —————————
( -25•35)
Dividing exponents :
3.1 28 divided by 25 = 2(8 - 5) = 23
Dividing exponents :
3.2 38 divided by 35 = 3(8 - 5) = 33
Final result :
-216
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