Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "^-3" was replaced by "^(-3)".

(2): "91.44" was replaced by "(9144/100)". 2 more similar replacement(s)

Step  1  :

            2286
 Simplify   ————
             25 

Equation at the end of step  1  :

   153             2286
  (——— • (10-3)) ÷ ————
   100              25 

Step  2  :

 2.1     10 = 2•5

(10)^-3 = (2•5)^(-3) = (2)^(-3) • (5)^(-3)

Equation at the end of step  2  :

   153                        2286
  (——— • ((2)(-3)•(5)(-3))) ÷ ————
   100                         25 

Step  3  :

            153
 Simplify   ———
            100

Equation at the end of step  3  :

  153                        2286
  ——— • ((2)(-3)•(5)(-3))) ÷ ————
  100                         25 

Step  4  :

Multiplying exponents :

 4.1    2²  multiplied by  2³   = 2^{(2 + 3)} = 2⁵

Multiplying exponents :

 4.2    5²  multiplied by  5³   = 5^{(2 + 3)} = 5⁵

Equation at the end of step  4  :

    153     2286
  ——————— ÷ ————
  (25•55)    25 

Step  5  :

           153        2286
 Divide  ———————  by  ————
         (25•55)       25 

 5.1    Dividing fractions

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

  153       2286         153        25 
———————  ÷  ————   =   ———————  •  ————
(25•55)      25        (25•55)     2286

Multiplying exponents :

 5.2    2⁵  multiplied by  2¹   = 2^{(5 + 1)} = 2⁶

Canceling Out :

 5.3      Canceling out  3² as it appears on both sides of the fraction line

Dividing exponents :

 5.4    5²   divided by   5⁵   = 5^{(2 - 5)} = 5^(-3) = ¹/_5³

Final result :

       17               
  ——————————— = 0.00002 
  (26•53•127)