Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

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

(2): "7.5" was replaced by "(75/10)".

Step  1  :

 1.1     10 = 2•5

(10)³ = (2•5)³ = 2³ • 5³

Equation at the end of step  1  :

                   75
  (5 • (10-2)) -  (—— • (23•53))
                   10

Step  2  :

            15
 Simplify   ——
            2 

Equation at the end of step  2  :

                   15
  (5 • (10-2)) -  (—— • (23•53))
                   2 

Step  3  :

Multiplying exponents :

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

Raising to a Power :

 3.2    2³   divided by   2¹   = 2^{(3 - 1)} = 2²

Equation at the end of step  3  :

  (5 • (10-2)) -  7500

Step  4  :

 4.1     10 = 2•5

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

Equation at the end of step  4  :

  (5 • ((2)(-2)•(5)(-2))) -  7500

Step  5  :

Dividing exponents :

 5.1    5¹   divided by   5²   = 5^{(1 - 2)} = 5^(-1) = ¹/_5¹ = ¹/₅

Equation at the end of step  5  :

   1    
  —— -  7500
  20    

Step  6  :

Rewriting the whole as an Equivalent Fraction :

 6.1   Subtracting a whole from a fraction

Rewrite the whole as a fraction using  20  as the denominator :

            7500     7500 • 20
    7500 =  ————  =  —————————
             1          20    

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:

 1 - (7500 • 20)     -149999
 ———————————————  =  ———————
       20              20   

Final result :

  -149999               
  ——————— = -7499.95000 
    20