Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "^-8" was replaced by "^(-8)".

(2): "0.9" was replaced by "(9/10)". 2 more similar replacement(s)

Step  1  :

 1.1     10 = 2•5

(10)⁷ = (2•5)⁷ = 2⁷ • 5⁷

Equation at the end of step  1  :

   117         9
  (———•(10-8))——•(27•57))
   100(       10

Step  2  :

             9
 Simplify   ——
            10

Equation at the end of step  2  :

   117               9
  (——— • (10-8)) ÷ (—— • (27•57))
   100              10

Step  3  :

Dividing exponents :

 3.1    2⁷   divided by   2¹   = 2^{(7 - 1)} = 2⁶

Raising to a Power :

 3.2    5⁷   divided by   5¹   = 5^{(7 - 1)} = 5⁶

Equation at the end of step  3  :

   117
  (——— • (10-8)) ÷ (32•26•56)
   100

Step  4  :

 4.1     10 = 2•5

(10)^-8 = (2•5)^(-8) = (2)^(-8) • (5)^(-8)

Equation at the end of step  4  :

   117
  (——— • ((2)(-8)•(5)(-8))) ÷ (32•26•56)
   100

Step  5  :

            117
 Simplify   ———
            100

Equation at the end of step  5  :

  117
  ——— • ((2)(-8)•(5)(-8))) ÷ (32•26•56)
  100

Step  6  :

Multiplying exponents :

 6.1    2²  multiplied by  2⁸   = 2^{(2 + 8)} = 2¹⁰

Multiplying exponents :

 6.2    5²  multiplied by  5⁸   = 5^{(2 + 8)} = 5¹⁰

Equation at the end of step  6  :

     117   
  ————————— ÷ (32•26•56)
  (210•510) 

Step  7  :

            117         
 Divide  —————————  by  (32•26•56)
         (210•510)       

Multiplying exponents :

 7.1    2¹⁰  multiplied by  2⁶   = 2^{(10 + 6)} = 2¹⁶

Multiplying exponents :

 7.2    5¹⁰  multiplied by  5⁶   = 5^{(10 + 6)} = 5¹⁶

Canceling Out :

 7.3      Canceling out  3² as it appears on both sides of the fraction line

Final result :

      13                                      
  ————————— = 1.30000 • 10-15 
  (216•516)