Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "^-2" was replaced by "^(-2)".

(2): "2.5" was replaced by "(25/10)". 2 more similar replacement(s)

Step  1  :

 1.1     10 = 2•5

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

Equation at the end of step  1  :

   63         25
  (——•(105))•(——•((2)(-2)•(5)(-2)))
   10         10

Step  2  :

            5
 Simplify   —
            2

Equation at the end of step  2  :

   63             5
  (—— • (105)) • (— • ((2)(-2)•(5)(-2)))
   10             2

Step  3  :

Multiplying exponents :

 3.1    2¹  multiplied by  2²   = 2^{(1 + 2)} = 2³

Raising to a Power :

 3.2    5¹   divided by   5²   = 5^{(1 - 2)} = 5^(-1) = ¹/_5¹ = ¹/₅

Equation at the end of step  3  :

   63             1
  (—— • (105)) • ——
   10            40

Step  4  :

 4.1     10 = 2•5

(10)⁵ = (2•5)⁵ = 2⁵ • 5⁵

Equation at the end of step  4  :

   63               1
  (—— • (25•55)) • ——
   10              40

Step  5  :

            63
 Simplify   ——
            10

Equation at the end of step  5  :

   63               1
  (—— • (25•55)) • ——
   10              40

Step  6  :

Dividing exponents :

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

Dividing exponents :

 6.2    5⁵   divided by   5¹   = 5^{(5 - 1)} = 5⁴

Equation at the end of step  6  :

                  1
  (32•7•24•54) • ——
                 40

Step  7  :

Dividing exponents :

 7.1    2⁴   divided by   2³   = 2^{(4 - 3)} = 2¹ = 2

Dividing exponents :

 7.2    5⁴   divided by   5¹   = 5^{(4 - 1)} = 5³

Final result :

  (32•7•2•53)