Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "2.5" was replaced by "(25/10)".

Step  1  :

 1.1     10 = 2•5

(10)¹⁰ = (2•5)¹⁰ = 2¹⁰ • 5¹⁰

Equation at the end of step  1  :

                 25
  (4 • (102)) • (—— • (210•510))
                 10

Step  2  :

            5
 Simplify   —
            2

Equation at the end of step  2  :

                 5
  (4 • (102)) • (— • (210•510))
                 2

Step  3  :

Multiplying exponents :

 3.1    5¹  multiplied by  5¹⁰   = 5^{(1 + 10)} = 5¹¹

Raising to a Power :

 3.2    2¹⁰   divided by   2¹   = 2^{(10 - 1)} = 2⁹

Equation at the end of step  3  :

  (4 • (102)) • (511•29)

Step  4  :

 4.1     10 = 2•5

(10)² = (2•5)² = 2² • 5²

Equation at the end of step  4  :

  (4 • (22•52)) • (511•29)

Step  5  :

Multiplying exponents :

 5.1    2²  multiplied by  2²   = 2^{(2 + 2)} = 2⁴

Equation at the end of step  5  :

  (24•52) • (511•29)

Step  6  :

Multiplying exponents :

 6.1    2⁴  multiplied by  2⁹   = 2^{(4 + 9)} = 2¹³

Multiplying exponents :

 6.2    5²  multiplied by  5¹¹   = 5^{(2 + 11)} = 5¹³

Final result :

  (213•513)