Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

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

(2): "2.52" was replaced by "(252/100)".

Step  1  :

 1.1     10 = 2•5

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

Equation at the end of step  1  :

   252
  (——— • (105)) • (4 • ((2)(-3)•(5)(-3)))
   100

Step  2  :

Raising to a Power :

 2.1    2²   divided by   2³   = 2^{(2 - 3)} = 2^(-1) = ¹/_2¹ = ¹/₂

Equation at the end of step  2  :

   252             1 
  (——— • (105)) • ———
   100            250

Step  3  :

 3.1     10 = 2•5

(10)⁵ = (2•5)⁵ = 2⁵ • 5⁵

Equation at the end of step  3  :

   252               1 
  (——— • (25•55)) • ———
   100              250

Step  4  :

            63
 Simplify   ——
            25

Equation at the end of step  4  :

   63               1 
  (—— • (25•55)) • ———
   25              250

Step  5  :

Dividing exponents :

 5.1    5⁵   divided by   5²   = 5^{(5 - 2)} = 5³

Equation at the end of step  5  :

                  1 
  (32•7•25•53) • ———
                 250

Step  6  :

Dividing exponents :

 6.1    2⁵   divided by   2¹   = 2^{(5 - 1)} = 2⁴

Canceling Out :

 6.2      Canceling out  5³ as it appears on both sides of the fraction line

Final result :

  1008