Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

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

(2): "2.52" was replaced by "(252/100)".

Step  1  :

 1.1     10 = 2•5

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

Equation at the end of step  1  :

   252              
  (——— • (105)) -  (4 • ((2)(-3)•(5)(-3)))
   100              

Step  2  :

Raising to a Power :

 2.1    2²   divided by   2³   = 2^{(2 - 3)} = 2^(-1) = ¹/_2¹ = ¹/₂

Equation at the end of step  2  :

   252              1 
  (——— • (105)) -  ———
   100             250

Step  3  :

 3.1     10 = 2•5

(10)⁵ = (2•5)⁵ = 2⁵ • 5⁵

Equation at the end of step  3  :

   252                1 
  (——— • (25•55)) -  ———
   100               250

Step  4  :

            63
 Simplify   ——
            25

Equation at the end of step  4  :

   63                1 
  (—— • (25•55)) -  ———
   25               250

Step  5  :

Dividing exponents :

 5.1    5⁵   divided by   5²   = 5^{(5 - 2)} = 5³

Equation at the end of step  5  :

                   1 
  (32•7•25•53) -  ———
                  250

Step  6  :

Rewriting the whole as an Equivalent Fraction :

 6.1   Subtracting a fraction from a whole

Rewrite the whole as a fraction using  250  as the denominator :

                     (32•7•25•53)      (32•7•25•53) • 250 
     (32•7•25•53) =  ————————————  =  ——————————————————
                          1                  250        

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:

Multiplying exponents :

 2⁵  multiplied by  2¹   = 2^{(5 + 1)} = 2⁶

Multiplying exponents :

 5³  multiplied by  5³   = 5^{(3 + 3)} = 5⁶ (3²•7•2⁵•5³) • 250 - (1) 3²•7•2⁶•5⁶ - 1 ———————————————————————— = —————————————— 250 250

Final result :

  63 - 1
  ——————
   250