Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

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

(2): "6.9" was replaced by "(69/10)".

Step  1  :

 1.1     10 = 2•5

(10)³ = (2•5)³ = 2³ • 5³

Equation at the end of step  1  :

                   69
  (8 • (10-1)) +  (—— • (23•53))
                   10

Step  2  :

            69
 Simplify   ——
            10

Equation at the end of step  2  :

                   69
  (8 • (10-1)) +  (—— • (23•53))
                   10

Step  3  :

Dividing exponents :

 3.1    2³   divided by   2¹   = 2^{(3 - 1)} = 2²

Raising to a Power :

 3.2    5³   divided by   5¹   = 5^{(3 - 1)} = 5²

Equation at the end of step  3  :

  (8 • (10-1)) +  6900

Step  4  :

 4.1     10 = 2•5

(10)^-1 = (2•5)^(-1) = (2)^(-1) • (5)^(-1)

Equation at the end of step  4  :

  (8 • ((2)(-1)•(5)(-1))) +  6900

Step  5  :

Dividing exponents :

 5.1    2³   divided by   2¹   = 2^{(3 - 1)} = 2²

Equation at the end of step  5  :

  4    
  — +  6900
  5    

Step  6  :

Rewriting the whole as an Equivalent Fraction :

 6.1   Adding a whole to a fraction

Rewrite the whole as a fraction using  5  as the denominator :

            6900     6900 • 5
    6900 =  ————  =  ————————
             1          5    

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 :

 6.2       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:

 4 + 6900 • 5     34504
 ————————————  =  —————
      5             5  

Final result :

  34504              
  ————— = 6900.80000 
    5