Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "^-9" was replaced by "^(-9)". 1 more similar replacement(s)

(2): "7.2" was replaced by "(72/10)". 2 more similar replacement(s)

Step  1  :

 1.1     10 = 2•5

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

Equation at the end of step  1  :

   61        72
  (——•(10-5))——•((2)(-9)•(5)(-9)))
   10(       10

Step  2  :

            36
 Simplify   ——
            5 

Equation at the end of step  2  :

   61              36
  (—— • (10-5)) ÷ (—— • ((2)(-9)•(5)(-9)))
   10              5 

Step  3  :

Multiplying exponents :

 3.1    5¹  multiplied by  5⁹   = 5^{(1 + 9)} = 5¹⁰

Raising to a Power :

 3.2    2²   divided by   2⁹   = 2^{(2 - 9)} = 2^(-7) = ¹/_2⁷

Equation at the end of step  3  :

   61                 9   
  (—— • (10-5)) ÷ ————————
   10             (510•27) 

Step  4  :

 4.1     10 = 2•5

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

Equation at the end of step  4  :

   61                            9   
  (—— • ((2)(-5)•(5)(-5))) ÷ ————————
   10                        (510•27) 

Step  5  :

            61
 Simplify   ——
            10

Equation at the end of step  5  :

  61                            9   
  —— • ((2)(-5)•(5)(-5))) ÷ ————————
  10                        (510•27) 

Step  6  :

Multiplying exponents :

 6.1    2¹  multiplied by  2⁵   = 2^{(1 + 5)} = 2⁶

Multiplying exponents :

 6.2    5¹  multiplied by  5⁵   = 5^{(1 + 5)} = 5⁶

Equation at the end of step  6  :

     61         9   
  ——————— ÷ ————————
  (26•56)   (510•27) 

Step  7  :

            61            9   
 Divide  ———————  by  ————————
         (26•56)      (510•27) 

 7.1    Dividing fractions

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

   61           9             61       (510•27) 
———————  ÷  ————————   =   ———————  •  ————————
(26•56)     (510•27)        (26•56)        9    

Dividing exponents :

 7.2    5¹⁰   divided by   5⁶   = 5^{(10 - 6)} = 5⁴

Dividing exponents :

 7.3    2⁷   divided by   2⁶   = 2^{(7 - 6)} = 2¹ = 2

Final result :

  (61•54•2)              
  ————————— = 8472.22222 
      9