Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "3.08" was replaced by "(308/100)". 2 more similar replacement(s)

Step  1  :

 1.1     10 = 2•5

(10)¹² = (2•5)¹² = 2¹² • 5¹²

Equation at the end of step  1  :

   215         308
  (———•(105))•(———•(212•512))
   100         100

Step  2  :

            77
 Simplify   ——
            25

Equation at the end of step  2  :

   215             77
  (——— • (105)) • (—— • (212•512))
   100             25

Step  3  :

Raising to a Power :

 3.1    5¹²   divided by   5²   = 5^{(12 - 2)} = 5¹⁰

Equation at the end of step  3  :

   215
  (——— • (105)) • (7•11•212•510)
   100

Step  4  :

 4.1     10 = 2•5

(10)⁵ = (2•5)⁵ = 2⁵ • 5⁵

Equation at the end of step  4  :

   215
  (——— • (25•55)) • (7•11•212•510)
   100

Step  5  :

            43
 Simplify   ——
            20

Equation at the end of step  5  :

   43
  (—— • (25•55)) • (7•11•212•510)
   20

Step  6  :

Dividing exponents :

 6.1    2⁵   divided by   2²   = 2^{(5 - 2)} = 2³

Dividing exponents :

 6.2    5⁵   divided by   5¹   = 5^{(5 - 1)} = 5⁴

Equation at the end of step  6  :

  (43•23•54) • (7•11•212•510)

Step  7  :

Multiplying exponents :

 7.1    2³  multiplied by  2¹²   = 2^{(3 + 12)} = 2¹⁵

Multiplying exponents :

 7.2    5⁴  multiplied by  5¹⁰   = 5^{(4 + 10)} = 5¹⁴

Final result :

  (43•215•514•7•11)