Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "^-14" was replaced by "^(-14)".

(2): "4.2" was replaced by "(42/10)". 2 more similar replacement(s)

Step  1  :

 1.1     10 = 2•5

(10)^-14 = (2•5)^(-14) = (2)^(-14) • (5)^(-14)

Equation at the end of step  1  :

   35         42
  (——•(109))•(——•((2)(-14)•(5)(-14)))
   10         10

Step  2  :

            21
 Simplify   ——
            5 

Equation at the end of step  2  :

   35             21
  (—— • (109)) • (—— • ((2)(-14)•(5)(-14)))
   10             5 

Step  3  :

Raising to a Power :

 3.1    5¹  multiplied by  5¹⁴   = 5^{(1 + 14)} = 5¹⁵

Equation at the end of step  3  :

   35                21   
  (—— • (109)) • —————————
   10            (515•214) 

Step  4  :

 4.1     10 = 2•5

(10)⁹ = (2•5)⁹ = 2⁹ • 5⁹

Equation at the end of step  4  :

   35                  21   
  (—— • (29•59)) • —————————
   10              (515•214) 

Step  5  :

            7
 Simplify   —
            2

Equation at the end of step  5  :

   7                  21   
  (— • (29•59)) • —————————
   2              (515•214) 

Step  6  :

Dividing exponents :

 6.1    2⁹   divided by   2¹   = 2^{(9 - 1)} = 2⁸

Equation at the end of step  6  :

                  21   
  (7•28•59) • —————————
              (515•214) 

Step  7  :

Multiplying exponents :

 7.1    7¹  multiplied by  7¹   = 7^{(1 + 1)} = 7²

Dividing exponents :

 7.2    2⁸   divided by   2¹⁴   = 2^{(8 - 14)} = 2^(-6) = ¹/_2⁶

Dividing exponents :

 7.3    5⁹   divided by   5¹⁵   = 5^{(9 - 15)} = 5^(-6) = ¹/_5⁶

Final result :

    147             
  ——————— = 0.00015 
  (56•26)