Step by Step Solution
Reformatting the input :
Changes made to your input should not affect the solution:
(1): "^-5" was replaced by "^(-5)".
Step 1 :
1.1 Raising to a negative exponent Raising a number to a negative exponent means 1 over that same number but now with a positive exponent. For example, x(-5) is equal to 1/x(5) 1.2
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
1.3 4 = 22 (-4)-5 = (22)(-5) = (2)(-10)
Equation at the end of step 1 :
(-48) • -(2)(-10)
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 4 = 22 (-4)8 = (22)8 = 216
Equation at the end of step 2 :
216 • -(2)(-10)
Step 3 :
Dividing exponents :
3.1 216 divided by 210 = 2(16 - 10) = 26
Final result :
-64
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