Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "*-10" was replaced by "*(-10)".

(2): "6.4" was replaced by "(64/10)".

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  :

  64
  —— • ( -23•53)
  10

Step  2  :

            32
 Simplify   ——
            5 

Equation at the end of step  2  :

  32
  —— • ( -23•53)
  5 

Step  3  :

Multiplying exponents :

 3.1    2⁵  multiplied by  2³   = 2^{(5 + 3)} = 2⁸

Dividing exponents :

 3.2    5³   divided by   5¹   = 5^{(3 - 1)} = 5²

Final result :

  -6400