Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "5.9" was replaced by "(59/10)". 2 more similar replacement(s)

Step  1  :

 1.1     10 = 2•5

(10)³ = (2•5)³ = 2³ • 5³

Equation at the end of step  1  :

   2065       59
  (————•(106))——•(23•53))
   1000(      10

Step  2  :

            59
 Simplify   ——
            10

Equation at the end of step  2  :

   2065             59
  (———— • (106)) ÷ (—— • (23•53))
   1000             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  :

   2065
  (———— • (106)) ÷ 5900
   1000

Step  4  :

 4.1     10 = 2•5

(10)⁶ = (2•5)⁶ = 2⁶ • 5⁶

Equation at the end of step  4  :

   2065
  (———— • (26•56)) ÷ 5900
   1000

Step  5  :

            413
 Simplify   ———
            200

Equation at the end of step  5  :

  413
  ——— • (26•56)) ÷ 5900
  200

Step  6  :

Dividing exponents :

 6.1    2⁶   divided by   2³   = 2^{(6 - 3)} = 2³

Dividing exponents :

 6.2    5⁶   divided by   5²   = 5^{(6 - 2)} = 5⁴

Equation at the end of step  6  :

Step  7  :

            (7•59•23•54)
 Simplify   ————————————
                5900    

Canceling Out :

 7.1      Canceling out  59  as it appears on both sides of the fraction line

Dividing exponents :

 7.2    2³   divided by   2²   = 2^{(3 - 2)} = 2¹ = 2

Dividing exponents :

 7.3    5⁴   divided by   5²   = 5^{(4 - 2)} = 5²

Final result :

  350