Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "3.2" was replaced by "(32/10)".

Step  1  :

 1.1     10 = 2•5

(10)¹³ = (2•5)¹³ = 2¹³ • 5¹³

Equation at the end of step  1  :

   32
  (—— • (109)) • (4 • (213•513))
   10

Step  2  :

Raising to a Power :

 2.1    2²  multiplied by  2¹³   = 2^{(2 + 13)} = 2¹⁵

Equation at the end of step  2  :

   32
  (—— • (109)) • (215•513)
   10

Step  3  :

 3.1     10 = 2•5

(10)⁹ = (2•5)⁹ = 2⁹ • 5⁹

Equation at the end of step  3  :

   32
  (—— • (29•59)) • (215•513)
   10

Step  4  :

            16
 Simplify   ——
            5 

Equation at the end of step  4  :

   16
  (—— • (29•59)) • (215•513)
   5 

Step  5  :

Multiplying exponents :

 5.1    2⁴  multiplied by  2⁹   = 2^{(4 + 9)} = 2¹³

Dividing exponents :

 5.2    5⁹   divided by   5¹   = 5^{(9 - 1)} = 5⁸

Equation at the end of step  5  :

  (213•58) • (215•513)

Step  6  :

Multiplying exponents :

 6.1    2¹³  multiplied by  2¹⁵   = 2^{(13 + 15)} = 2²⁸

Multiplying exponents :

 6.2    5⁸  multiplied by  5¹³   = 5^{(8 + 13)} = 5²¹

Final result :

  (228•521)