Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

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

(2): "2.4" was replaced by "(24/10)". 2 more similar replacement(s)

Step  1  :

 1.1     10 = 2•5

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

Equation at the end of step  1  :

   63         24
  (——•(102))-(——•((2)(-3)•(5)(-3)))
   10         10

Step  2  :

            12
 Simplify   ——
            5 

Equation at the end of step  2  :

   63              12
  (—— • (102)) -  (—— • ((2)(-3)•(5)(-3)))
   10              5 

Step  3  :

Multiplying exponents :

 3.1    5¹  multiplied by  5³   = 5^{(1 + 3)} = 5⁴

Raising to a Power :

 3.2    2²   divided by   2³   = 2^{(2 - 3)} = 2^(-1) = ¹/_2¹ = ¹/₂

Equation at the end of step  3  :

   63               3 
  (—— • (102)) -  ————
   10             1250

Step  4  :

 4.1     10 = 2•5

(10)² = (2•5)² = 2² • 5²

Equation at the end of step  4  :

   63                 3 
  (—— • (22•52)) -  ————
   10               1250

Step  5  :

            63
 Simplify   ——
            10

Equation at the end of step  5  :

   63                 3 
  (—— • (22•52)) -  ————
   10               1250

Step  6  :

Dividing exponents :

 6.1    2²   divided by   2¹   = 2^{(2 - 1)} = 2¹ = 2

Dividing exponents :

 6.2    5²   divided by   5¹   = 5^{(2 - 1)} = 5¹ = 5

Equation at the end of step  6  :

           3 
  630 -  ————
         1250

Step  7  :

Rewriting the whole as an Equivalent Fraction :

 7.1   Subtracting a fraction from a whole

Rewrite the whole as a fraction using  1250  as the denominator :

            630     630 • 1250
     630 =  ———  =  ——————————
             1         1250   

Equivalent fraction : The fraction thus generated looks different but has the same value as the whole

Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator

Adding fractions that have a common denominator :

 7.2       Adding up the two equivalent fractions
Add the two equivalent fractions which now have a common denominator

Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

 630 • 1250 - (3)     787497
 ————————————————  =  ——————
       1250            1250 

Final result :

  787497             
  —————— = 629.99760 
   1250