Solution - Simplification or other simple results
5^6/192=81.38021
Step by Step Solution
Step 1 :
125
Simplify ———
8
Equation at the end of step 1 :
125
———)2) ÷ 3
8
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
2.2 125 = 53 (-125)2 = (53)2 = 56 2.3 8 = 23 (8)2 = (23)2 = 26
Equation at the end of step 2 :
56
—— ÷ 3
26
Step 3 :
56
Divide —— by 3
26
Final result :
56
——— = 81.38021
192
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