Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "^-3" was replaced by "^(-3)".

(2): "6.25" was replaced by "(625/100)".

Step  1  :

 1.1     10 = 2•5

(10)^-3 = (2•5)^(-3) = (2)^(-3) • (5)^(-3)

Equation at the end of step  1  :

  625
  ——— • ((2)(-3)•(5)(-3))
  100

Step  2  :

            25
 Simplify   ——
            4 

Equation at the end of step  2  :

  25
  —— • ((2)(-3)•(5)(-3))
  4 

Step  3  :

Multiplying exponents :

 3.1    2²  multiplied by  2³   = 2^{(2 + 3)} = 2⁵

Dividing exponents :

 3.2    5²   divided by   5³   = 5^{(2 - 3)} = 5^(-1) = ¹/_5¹ = ¹/₅

Final result :

   1            
  ——— = 0.00625 
  160