Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "^-2" was replaced by "^(-2)".

(2): "0.078" was replaced by "(078/1000)". 2 more similar replacement(s)

Step  1  :

 1.1     10 = 2•5

(10)³ = (2•5)³ = 2³ • 5³

Equation at the end of step  1  :

   59           78 
  (——•(10-2))-(————•(23•53))
   10          1000

Step  2  :

             39
 Simplify   ———
            500

Equation at the end of step  2  :

   59                39
  (—— • (10-2)) -  (——— • (23•53))
   10               500

Step  3  :

Dividing exponents :

 3.1    2³   divided by   2²   = 2^{(3 - 2)} = 2¹ = 2

Raising to a Power :

 3.2      Canceling out  5³ as it appears on both sides of the fraction line

Equation at the end of step  3  :

   59               
  (—— • (10-2)) -  78
   10               

Step  4  :

 4.1     10 = 2•5

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

Equation at the end of step  4  :

   59                           
  (—— • ((2)(-2)•(5)(-2))) -  78
   10                           

Step  5  :

            59
 Simplify   ——
            10

Equation at the end of step  5  :

   59                           
  (—— • ((2)(-2)•(5)(-2))) -  78
   10                           

Step  6  :

Multiplying exponents :

 6.1    2¹  multiplied by  2²   = 2^{(1 + 2)} = 2³

Multiplying exponents :

 6.2    5¹  multiplied by  5²   = 5^{(1 + 2)} = 5³

Equation at the end of step  6  :

   59     
  ———— -  78
  1000    

Step  7  :

Rewriting the whole as an Equivalent Fraction :

 7.1   Subtracting a whole from a fraction

Rewrite the whole as a fraction using  1000  as the denominator :

          78     78 • 1000
    78 =  ——  =  —————————
          1        1000   

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:

 59 - (78 • 1000)     -77941
 ————————————————  =  ——————
       1000            1000 

Final result :

  -77941             
  —————— = -77.94100 
   1000