Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

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

(2): "3." was replaced by "(3/1)". 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  :

   39       3
  (——•(104))—•((2)(-2)•(5)(-2)))
   10(      1

Step  2  :

            3
 Simplify   —
            1

Equation at the end of step  2  :

   39
  (—— • (104)) ÷ (3 • ((2)(-2)•(5)(-2)))
   10

Step  3  :

Equation at the end of step  3  :

   39             3 
  (—— • (104)) ÷ ———
   10            100

Step  4  :

 4.1     10 = 2•5

(10)⁴ = (2•5)⁴ = 2⁴ • 5⁴

Equation at the end of step  4  :

   39               3 
  (—— • (24•54)) ÷ ———
   10              100

Step  5  :

            39
 Simplify   ——
            10

Equation at the end of step  5  :

  39               3 
  —— • (24•54)) ÷ ———
  10              100

Step  6  :

Dividing exponents :

 6.1    2⁴   divided by   2¹   = 2^{(4 - 1)} = 2³

Dividing exponents :

 6.2    5⁴   divided by   5¹   = 5^{(4 - 1)} = 5³

Equation at the end of step  6  :

  )3 
  ———
  100

Step  7  :

                            3 
 Divide  (3•13•23•53)  by  ———
                           100

Multiplying exponents :

 7.1    2³  multiplied by  2²   = 2^{(3 + 2)} = 2⁵

Multiplying exponents :

 7.2    5³  multiplied by  5²   = 5^{(3 + 2)} = 5⁵

Canceling Out :

 7.3      Canceling out  3  as it appears on both sides of the fraction line

Final result :

  (13•25•55)