Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "3.7" was replaced by "(37/10)".

Step  1  :

 1.1     10 = 2•5

(10)³ = (2•5)³ = 2³ • 5³

Equation at the end of step  1  :

                 37
  (2 • (106)) • (—— • (23•53))
                 10

Step  2  :

            37
 Simplify   ——
            10

Equation at the end of step  2  :

                 37
  (2 • (106)) • (—— • (23•53))
                 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  :

  (2 • (106)) • 3700

Step  4  :

 4.1     10 = 2•5

(10)⁶ = (2•5)⁶ = 2⁶ • 5⁶

Equation at the end of step  4  :

  (2 • (26•56)) • 3700

Step  5  :

Multiplying exponents :

 5.1    2¹  multiplied by  2⁶   = 2^{(1 + 6)} = 2⁷

Equation at the end of step  5  :

  (27•56) • 3700

Step  6  :

Multiplying exponents :

 6.1    2⁷  multiplied by  2²   = 2^{(7 + 2)} = 2⁹

Multiplying exponents :

 6.2    5⁶  multiplied by  5²   = 5^{(6 + 2)} = 5⁸

Final result :

  (29•58•37)