Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "1.6" was replaced by "(16/10)". 2 more similar replacement(s)

Step  1  :

 1.1     10 = 2•5

(10)⁶ = (2•5)⁶ = 2⁶ • 5⁶

Equation at the end of step  1  :

   32         16
  (——•(102))•(——•(26•56))
   10         10

Step  2  :

            8
 Simplify   —
            5

Equation at the end of step  2  :

   32             8
  (—— • (102)) • (— • (26•56))
   10             5

Step  3  :

Multiplying exponents :

 3.1    2³  multiplied by  2⁶   = 2^{(3 + 6)} = 2⁹

Raising to a Power :

 3.2    5⁶   divided by   5¹   = 5^{(6 - 1)} = 5⁵

Equation at the end of step  3  :

   32
  (—— • (102)) • (29•55)
   10

Step  4  :

 4.1     10 = 2•5

(10)² = (2•5)² = 2² • 5²

Equation at the end of step  4  :

   32
  (—— • (22•52)) • (29•55)
   10

Step  5  :

            16
 Simplify   ——
            5 

Equation at the end of step  5  :

   16
  (—— • (22•52)) • (29•55)
   5 

Step  6  :

Multiplying exponents :

 6.1    2⁴  multiplied by  2²   = 2^{(4 + 2)} = 2⁶

Dividing exponents :

 6.2    5²   divided by   5¹   = 5^{(2 - 1)} = 5¹ = 5

Equation at the end of step  6  :

  320 • (29•55)

Step  7  :

Multiplying exponents :

 7.1    2⁶  multiplied by  2⁹   = 2^{(6 + 9)} = 2¹⁵

Multiplying exponents :

 7.2    5¹  multiplied by  5⁵   = 5^{(1 + 5)} = 5⁶

Final result :

  (215•56)