Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "^-17" was replaced by "^(-17)".

(2): "4.5" was replaced by "(45/10)". 2 more similar replacement(s)

Step  1  :

 1.1     10 = 2•5

(10)¹³ = (2•5)¹³ = 2¹³ • 5¹³

Equation at the end of step  1  :

    506          45
  ((———•(10-17))•——)•(213•513)
    100          10

Step  2  :

            9
 Simplify   —
            2

Equation at the end of step  2  :

    506              9
  ((——— • (10-17)) • —) • (213•513)
    100              2

Step  3  :

 3.1     10 = 2•5

(10)^-17 = (2•5)^(-17) = (2)^(-17) • (5)^(-17)

Equation at the end of step  3  :

    506                          9
  ((——— • ((2)(-17)•(5)(-17))) • —) • (213•513)
    100                          2

Step  4  :

            253
 Simplify   ———
            50 

Equation at the end of step  4  :

    253                          9
  ((——— • ((2)(-17)•(5)(-17))) • —) • (213•513)
    50                           2

Step  5  :

Multiplying exponents :

 5.1    2¹  multiplied by  2¹⁷   = 2^{(1 + 17)} = 2¹⁸

Multiplying exponents :

 5.2    5²  multiplied by  5¹⁷   = 5^{(2 + 17)} = 5¹⁹

Equation at the end of step  5  :

      253      9
  (————————— • —) • (213•513)
   (218•519)    2

Step  6  :

Multiplying exponents :

 6.1    2¹⁸  multiplied by  2¹   = 2^{(18 + 1)} = 2¹⁹

Equation at the end of step  6  :

     2277  
  ————————— • (213•513)
  (219•519) 

Step  7  :

Dividing exponents :

 7.1    2¹³   divided by   2¹⁹   = 2^{(13 - 19)} = 2^(-6) = ¹/_2⁶

Dividing exponents :

 7.2    5¹³   divided by   5¹⁹   = 5^{(13 - 19)} = 5^(-6) = ¹/_5⁶

Final result :

    2277            
  ——————— = 0.00228 
  (26•56)