Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

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

(2): "5.3" was replaced by "(53/10)". 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  :

   706 53
  (———•——)•((2)(-2)•(5)(-2))
   100 10

Step  2  :

            53
 Simplify   ——
            10

Equation at the end of step  2  :

   706   53
  (——— • ——) • ((2)(-2)•(5)(-2))
   100   10

Step  3  :

 3.1     10 = 2•5

(10)⁵ = (2•5)⁵ = 2⁵ • 5⁵

Equation at the end of step  3  :

   706   53
  (——— • ——) • ((2)(-2)•(5)(-2))
   100   10

Step  4  :

                      53
 Divide  (25•55)  by  ——
                      10

Multiplying exponents :

 4.1    2⁵  multiplied by  2¹   = 2^{(5 + 1)} = 2⁶

Multiplying exponents :

 4.2    5⁵  multiplied by  5¹   = 5^{(5 + 1)} = 5⁶

Equation at the end of step  4  :

   706   (26•56)
  (——— • ———————) • ((2)(-2)•(5)(-2))
   100     53   

Step  5  :

            353
 Simplify   ———
            50 

Equation at the end of step  5  :

   353   (26•56)
  (——— • ———————) • ((2)(-2)•(5)(-2))
   50      53   

Step  6  :

Dividing exponents :

 6.1    2⁶   divided by   2¹   = 2^{(6 - 1)} = 2⁵

Dividing exponents :

 6.2    5⁶   divided by   5²   = 5^{(6 - 2)} = 5⁴

Equation at the end of step  6  :

  (353•25•54)
  ——————————— • ((2)(-2)•(5)(-2))
      53     

Step  7  :

Dividing exponents :

 7.1    2⁵   divided by   2²   = 2^{(5 - 2)} = 2³

Dividing exponents :

 7.2    5⁴   divided by   5²   = 5^{(4 - 2)} = 5²

Final result :

  (353•23•52)              
  ——————————— = 1332.07547 
      53