Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "^-6" was replaced by "^(-6)".

(2): "1.48" was replaced by "(148/100)".

Step  1  :

 1.1     300 = 22•3•52

(300)² = (2²•3•5²)² = 2⁴ • 3² • 5⁴

Equation at the end of step  1  :

   148
  (——— • (10-6)) • (24•32•54)
   100

Step  2  :

 2.1     10 = 2•5

(10)^-6 = (2•5)^(-6) = (2)^(-6) • (5)^(-6)

Equation at the end of step  2  :

   148
  (——— • ((2)(-6)•(5)(-6))) • (24•32•54)
   100

Step  3  :

            37
 Simplify   ——
            25

Equation at the end of step  3  :

   37
  (—— • ((2)(-6)•(5)(-6))) • (24•32•54)
   25

Step  4  :

Multiplying exponents :

 4.1    5²  multiplied by  5⁶   = 5^{(2 + 6)} = 5⁸

Equation at the end of step  4  :

     37  
  ——————— • (24•32•54)
  (58•26)

Step  5  :

Dividing exponents :

 5.1    2⁴   divided by   2⁶   = 2^{(4 - 6)} = 2^(-2) = ¹/_2²

Dividing exponents :

 5.2    5⁴   divided by   5⁸   = 5^{(4 - 8)} = 5^(-4) = ¹/_5⁴

Final result :

   333           
  ———— = 0.13320 
  2500