Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

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

(2): "4.4" was replaced by "(44/10)". 2 more similar replacement(s)

Step  1  :

            22
 Simplify   ——
            5 

Equation at the end of step  1  :

   132             22
  (——— • (10-3)) ÷ ——
   100             5 

Step  2  :

 2.1     10 = 2•5

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

Equation at the end of step  2  :

   132                        22
  (——— • ((2)(-3)•(5)(-3))) ÷ ——
   100                        5 

Step  3  :

            33
 Simplify   ——
            25

Equation at the end of step  3  :

  33                        22
  —— • ((2)(-3)•(5)(-3))) ÷ ——
  25                        5 

Step  4  :

Multiplying exponents :

 4.1    5²  multiplied by  5³   = 5^{(2 + 3)} = 5⁵

Equation at the end of step  4  :

     33     22
  ——————— ÷ ——
  (55•23)   5 

Step  5  :

            33        22
 Divide  ———————  by  ——
         (55•23)      5 

 5.1    Dividing fractions

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

   33       22          33        5
———————  ÷  ——   =   ———————  •  ——
(55•23)     5        (55•23)     22

Multiplying exponents :

 5.2    2³  multiplied by  2¹   = 2^{(3 + 1)} = 2⁴

Dividing exponents :

 5.3    5¹   divided by   5⁵   = 5^{(1 - 5)} = 5^(-4) = ¹/_5⁴

Canceling Out :

 5.4      Canceling out  11  as it appears on both sides of the fraction line

Final result :

     3              
  ——————— = 0.00030 
  (54•24)