Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "^-4" was replaced by "^(-4)".

(2): "1.77" was replaced by "(177/100)". 2 more similar replacement(s)

Step  1  :

 1.1     10 = 2•5

(10)^-4 = (2•5)^(-4) = (2)^(-4) • (5)^(-4)

Equation at the end of step  1  :

  588    177
  ——— ÷ (——— • ((2)(-4)•(5)(-4)))
  100    100

Step  2  :

            177
 Simplify   ———
            100

Equation at the end of step  2  :

  588    177
  ——— ÷ (——— • ((2)(-4)•(5)(-4)))
  100    100

Step  3  :

Multiplying exponents :

 3.1    2²  multiplied by  2⁴   = 2^{(2 + 4)} = 2⁶

Multiplying exponents :

 3.2    5²  multiplied by  5⁴   = 5^{(2 + 4)} = 5⁶

Equation at the end of step  3  :

  588     177  
  ——— ÷ ———————
  100   (26•56)

Step  4  :

            147
 Simplify   ———
            25 

Equation at the end of step  4  :

  147     177  
  ——— ÷ ———————
  25    (26•56)

Step  5  :

         147        177  
 Divide  ———  by  ———————
         25       (26•56)

 5.1    Dividing fractions

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

147       177         147     (26•56)
———  ÷  ———————   =   ———  •  ———————
25      (26•56)       25        177  

Canceling Out :

 5.2      Canceling out  3  as it appears on both sides of the fraction line

Dividing exponents :

 5.3    5⁶   divided by   5²   = 5^{(6 - 2)} = 5⁴

Final result :

  (72•26•54)                
  —————————— = 33220.33898 
      59