Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "2.1" was replaced by "(21/10)". 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  :

   63         21
  (——•(105))•(——•(23•53))
   10         10

Step  2  :

            21
 Simplify   ——
            10

Equation at the end of step  2  :

   63             21
  (—— • (105)) • (—— • (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  :

   63
  (—— • (105)) • 2100
   10

Step  4  :

 4.1     10 = 2•5

(10)⁵ = (2•5)⁵ = 2⁵ • 5⁵

Equation at the end of step  4  :

   63
  (—— • (25•55)) • 2100
   10

Step  5  :

            63
 Simplify   ——
            10

Equation at the end of step  5  :

   63
  (—— • (25•55)) • 2100
   10

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  :

  (32•7•24•54) • 2100

Step  7  :

Multiplying exponents :

 7.1    3²  multiplied by  3¹   = 3^{(2 + 1)} = 3³

Multiplying exponents :

 7.2    7¹  multiplied by  7¹   = 7^{(1 + 1)} = 7²

Multiplying exponents :

 7.3    2⁴  multiplied by  2²   = 2^{(4 + 2)} = 2⁶

Multiplying exponents :

 7.4    5⁴  multiplied by  5²   = 5^{(4 + 2)} = 5⁶

Final result :

  (33•72•26•56)