Solution - Power equations
Step by Step Solution
Reformatting the input :
Changes made to your input should not affect the solution:
(1): "*-10" was replaced by "*(-10)".
(2): "3.02" was replaced by "(302/100)".
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 10 = 2•5 (-10)3 = (2•5)3 = -23 • 53
Equation at the end of step 1 :
302
——— • ( -23•53)
100
Step 2 :
151
Simplify ———
50
Equation at the end of step 2 :
151
——— • ( -23•53)
50
Step 3 :
Dividing exponents :
3.1 23 divided by 21 = 2(3 - 1) = 22
Dividing exponents :
3.2 53 divided by 52 = 5(3 - 2) = 51 = 5
Final result :
-3020
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