Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "^-18" was replaced by "^(-18)".

(2): "5.625" was replaced by "(5625/1000)".

Step  1  :

 1.1     10 = 2•5

(10)^-18 = (2•5)^(-18) = (2)^(-18) • (5)^(-18)

Equation at the end of step  1  :

                  5625
  (4 • (1012)) • (———— • ((2)(-18)•(5)(-18)))
                  1000

Step  2  :

            45
 Simplify   ——
            8 

Equation at the end of step  2  :

                  45
  (4 • (1012)) • (—— • ((2)(-18)•(5)(-18)))
                  8 

Step  3  :

Multiplying exponents :

 3.1    2³  multiplied by  2¹⁸   = 2^{(3 + 18)} = 2²¹

Raising to a Power :

 3.2    5¹   divided by   5¹⁸   = 5^{(1 - 18)} = 5^(-17) = ¹/_5¹⁷

Equation at the end of step  3  :

                     9    
  (4 • (1012)) • —————————
                 (221•517) 

Step  4  :

 4.1     10 = 2•5

(10)¹² = (2•5)¹² = 2¹² • 5¹²

Equation at the end of step  4  :

                        9    
  (4 • (212•512)) • —————————
                    (221•517) 

Step  5  :

Multiplying exponents :

 5.1    2²  multiplied by  2¹²   = 2^{(2 + 12)} = 2¹⁴

Equation at the end of step  5  :

                  9    
  (214•512) • —————————
              (221•517) 

Step  6  :

Dividing exponents :

 6.1    2¹⁴   divided by   2²¹   = 2^{(14 - 21)} = 2^(-7) = ¹/_2⁷

Dividing exponents :

 6.2    5¹²   divided by   5¹⁷   = 5^{(12 - 17)} = 5^(-5) = ¹/_5⁵

Final result :

     9              
  ——————— = 0.00002 
  (27•55)