Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "^-15" was replaced by "^(-15)". 1 more similar replacement(s)

(2): "9.6" was replaced by "(96/10)".

Step  1  :

 1.1     10 = 2•5

(10)^-15 = (2•5)^(-15) = (2)^(-15) • (5)^(-15)

Equation at the end of step  1  :

   96
  (—— • (10-8)) ÷ (2 • ((2)(-15)•(5)(-15)))
   10

Step  2  :

Raising to a Power :

 2.1    2¹   divided by   2¹⁵   = 2^{(1 - 15)} = 2^(-14) = ¹/_2¹⁴

Equation at the end of step  2  :

   96                 1    
  (—— • (10-8)) ÷ —————————
   10             (214•515) 

Step  3  :

 3.1     10 = 2•5

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

Equation at the end of step  3  :

   96                            1    
  (—— • ((2)(-8)•(5)(-8))) ÷ —————————
   10                        (214•515) 

Step  4  :

            48
 Simplify   ——
            5 

Equation at the end of step  4  :

  48                            1    
  —— • ((2)(-8)•(5)(-8))) ÷ —————————
  5                         (214•515) 

Step  5  :

Multiplying exponents :

 5.1    5¹  multiplied by  5⁸   = 5^{(1 + 8)} = 5⁹

Dividing exponents :

 5.2    2⁴   divided by   2⁸   = 2^{(4 - 8)} = 2^(-4) = ¹/_2⁴

Equation at the end of step  5  :

     3          1    
  ——————— ÷ —————————
  (59•24)   (214•515) 

Step  6  :

            3             1    
 Divide  ———————  by  —————————
         (59•24)      (214•515) 

 6.1    Dividing fractions

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

   3            1              3        (214•515) 
———————  ÷  —————————   =   ———————  •  —————————
(59•24)     (214•515)        (59•24)         1    

Dividing exponents :

 6.2    2¹⁴   divided by   2⁴   = 2^{(14 - 4)} = 2¹⁰

Dividing exponents :

 6.3    5¹⁵   divided by   5⁹   = 5^{(15 - 9)} = 5⁶

Final result :

  (3•210•56)