Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "45.1" was replaced by "(451/10)". 2 more similar replacement(s)

Step  1  :

            451
 Simplify   ———
            10 

Equation at the end of step  1  :

   9133             451
  (———— • (106)) +  ———
   1000             10 

Step  2  :

 2.1     10 = 2•5

(10)⁶ = (2•5)⁶ = 2⁶ • 5⁶

Equation at the end of step  2  :

   9133               451
  (———— • (26•56)) +  ———
   1000               10 

Step  3  :

            9133
 Simplify   ————
            1000

Equation at the end of step  3  :

   9133               451
  (———— • (26•56)) +  ———
   1000               10 

Step  4  :

Dividing exponents :

 4.1    2⁶   divided by   2³   = 2^{(6 - 3)} = 2³

Dividing exponents :

 4.2    5⁶   divided by   5³   = 5^{(6 - 3)} = 5³

Equation at the end of step  4  :

                  451
  (9133•23•53) +  ———
                  10 

Step  5  :

Rewriting the whole as an Equivalent Fraction :

 5.1   Adding a fraction to a whole

Rewrite the whole as a fraction using  10  as the denominator :

                     (9133•23•53)     (9133•23•53) • 10
     (9133•23•53) =  ————————————  =  —————————————————
                          1                  10        

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 :

 5.2       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 :

 2³  multiplied by  2¹   = 2^{(3 + 1)} = 2⁴

Multiplying exponents :

 5³  multiplied by  5¹   = 5^{(3 + 1)} = 5⁴ (9133•2³•5³) • 10 + 451 9133•2⁴•5⁴ + 451 ——————————————————————— = ———————————————— 10 10

Final result :

  9133 + 451
  ——————————
      10