Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "3." was replaced by "(3/1)". 2 more similar replacement(s)

Step  1  :

 1.1     10 = 2•5

(10)⁵ = (2•5)⁵ = 2⁵ • 5⁵

Equation at the end of step  1  :

   51       3
  (——•(109))—•(25•55))
   10(      1

Step  2  :

            3
 Simplify   —
            1

Equation at the end of step  2  :

   51
  (—— • (109)) ÷ (3 • (25•55))
   10

Step  3  :

Equation at the end of step  3  :

   51
  (—— • (109)) ÷ (3•25•55)
   10

Step  4  :

 4.1     10 = 2•5

(10)⁹ = (2•5)⁹ = 2⁹ • 5⁹

Equation at the end of step  4  :

   51
  (—— • (29•59)) ÷ (3•25•55)
   10

Step  5  :

            51
 Simplify   ——
            10

Equation at the end of step  5  :

  51
  —— • (29•59)) ÷ (3•25•55)
  10

Step  6  :

Dividing exponents :

 6.1    2⁹   divided by   2¹   = 2^{(9 - 1)} = 2⁸

Dividing exponents :

 6.2    5⁹   divided by   5¹   = 5^{(9 - 1)} = 5⁸

Equation at the end of step  6  :

Step  7  :

            (3•17•28•58)
 Simplify   ————————————
             (3•25•55)  

Canceling Out :

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

Dividing exponents :

 7.2    2⁸   divided by   2⁵   = 2^{(8 - 5)} = 2³

Dividing exponents :

 7.3    5⁸   divided by   5⁵   = 5^{(8 - 5)} = 5³

Final result :

  (17•23•53)