Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "9.1" was replaced by "(91/10)". 2 more similar replacement(s)

Step  1  :

 1.1     10 = 2•5

(10)³ = (2•5)³ = 2³ • 5³

Equation at the end of step  1  :

   27         91
  (——•(104))•(——•(23•53))
   10         10

Step  2  :

            91
 Simplify   ——
            10

Equation at the end of step  2  :

   27             91
  (—— • (104)) • (—— • (23•53))
   10             10

Step  3  :

Dividing exponents :

 3.1    2³   divided by   2¹   = 2^{(3 - 1)} = 2²

Raising to a Power :

 3.2    5³   divided by   5¹   = 5^{(3 - 1)} = 5²

Equation at the end of step  3  :

   27
  (—— • (104)) • 9100
   10

Step  4  :

 4.1     10 = 2•5

(10)⁴ = (2•5)⁴ = 2⁴ • 5⁴

Equation at the end of step  4  :

   27
  (—— • (24•54)) • 9100
   10

Step  5  :

            27
 Simplify   ——
            10

Equation at the end of step  5  :

   27
  (—— • (24•54)) • 9100
   10

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  :

  (33•23•53) • 9100

Step  7  :

Multiplying exponents :

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

Multiplying exponents :

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

Final result :

  (33•25•55•7•13)