Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "^-9" was replaced by "^(-9)".

(2): "6.7" was replaced by "(67/10)".

Step  1  :

 1.1     10 = 2•5

(10)^-9 = (2•5)^(-9) = (2)^(-9) • (5)^(-9)

Equation at the end of step  1  :

                 67
  (4 • (108)) • (—— • ((2)(-9)•(5)(-9)))
                 10

Step  2  :

            67
 Simplify   ——
            10

Equation at the end of step  2  :

                 67
  (4 • (108)) • (—— • ((2)(-9)•(5)(-9)))
                 10

Step  3  :

Multiplying exponents :

 3.1    2¹  multiplied by  2⁹   = 2^{(1 + 9)} = 2¹⁰

Raising to a Power :

 3.2    5¹  multiplied by  5⁹   = 5^{(1 + 9)} = 5¹⁰

Equation at the end of step  3  :

                    67   
  (4 • (108)) • —————————
                (210•510) 

Step  4  :

 4.1     10 = 2•5

(10)⁸ = (2•5)⁸ = 2⁸ • 5⁸

Equation at the end of step  4  :

                      67   
  (4 • (28•58)) • —————————
                  (210•510) 

Step  5  :

Multiplying exponents :

 5.1    2²  multiplied by  2⁸   = 2^{(2 + 8)} = 2¹⁰

Equation at the end of step  5  :

                 67   
  (210•58) • —————————
             (210•510) 

Step  6  :

Canceling Out :

 6.1      Canceling out  2¹⁰ as it appears on both sides of the fraction line

Dividing exponents :

 6.2    5⁸   divided by   5¹⁰   = 5^{(8 - 10)} = 5^(-2) = ¹/_5²

Final result :

  67           
  —— = 2.68000 
  25