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)¹⁵ = (2•5)¹⁵ = 2¹⁵ • 5¹⁵

Equation at the end of step  1  :

  52   16   (1010) 
  —— ÷ ——•—————————
  10   10 (215•515)

Step  2  :

 2.1     10 = 2•5

(10)¹⁰ = (2•5)¹⁰ = 2¹⁰ • 5¹⁰

Equation at the end of step  2  :

  52   16   (210•510)
  —— ÷ —— • —————————
  10   10   (215•515)

Step  3  :

            (210•510)
 Simplify   —————————
            (215•515)

Dividing exponents :

 3.1    2¹⁰   divided by   2¹⁵   = 2^{(10 - 15)} = 2^(-5) = ¹/_2⁵

Dividing exponents :

 3.2    5¹⁰   divided by   5¹⁵   = 5^{(10 - 15)} = 5^(-5) = ¹/_5⁵

Equation at the end of step  3  :

  52   16      1   
  —— ÷ —— • ———————
  10   10   (25•55)

Step  4  :

            8
 Simplify   —
            5

Equation at the end of step  4  :

  52   8      1   
  —— ÷ — • ———————
  10   5   (25•55)

Step  5  :

            26
 Simplify   ——
            5 

Equation at the end of step  5  :

  26   8      1   
  —— ÷ — • ———————
  5    5   (25•55)

Step  6  :

         26      8
 Divide  ——  by  —
         5       5

 6.1    Dividing fractions

To divide fractions, write the divison as multiplication by the reciprocal of the divisor :

26     8       26     5
——  ÷  —   =   ——  •  —
5      5       5      8

Equation at the end of step  6  :

  13      1   
  —— • ———————
  4    (25•55)

Step  7  :

Multiplying exponents :

 7.1    2²  multiplied by  2⁵   = 2^{(2 + 5)} = 2⁷

Final result :

     13             
  ——————— = 0.00003 
  (27•55)