Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "2.65" was replaced by "(265/100)". 2 more similar replacement(s)

Step  1  :

 1.1     10 = 2•5

(10)⁴ = (2•5)⁴ = 2⁴ • 5⁴

Equation at the end of step  1  :

   106       265
  (———•(107))———•(24•54))
   100(      100

Step  2  :

            53
 Simplify   ——
            20

Equation at the end of step  2  :

   106             53
  (——— • (107)) ÷ (—— • (24•54))
   100             20

Step  3  :

Dividing exponents :

 3.1    2⁴   divided by   2²   = 2^{(4 - 2)} = 2²

Raising to a Power :

 3.2    5⁴   divided by   5¹   = 5^{(4 - 1)} = 5³

Equation at the end of step  3  :

   106
  (——— • (107)) ÷ (53•22•53)
   100

Step  4  :

 4.1     10 = 2•5

(10)⁷ = (2•5)⁷ = 2⁷ • 5⁷

Equation at the end of step  4  :

   106
  (——— • (27•57)) ÷ (53•22•53)
   100

Step  5  :

            53
 Simplify   ——
            50

Equation at the end of step  5  :

  53
  —— • (27•57)) ÷ (53•22•53)
  50

Step  6  :

Dividing exponents :

 6.1    2⁷   divided by   2¹   = 2^{(7 - 1)} = 2⁶

Dividing exponents :

 6.2    5⁷   divided by   5²   = 5^{(7 - 2)} = 5⁵

Equation at the end of step  6  :

Step  7  :

            (53•26•55)
 Simplify   ——————————
            (53•22•53)

Canceling Out :

 7.1      Canceling out  53  as it appears on both sides of the fraction line

Dividing exponents :

 7.2    2⁶   divided by   2²   = 2^{(6 - 2)} = 2⁴

Dividing exponents :

 7.3    5⁵   divided by   5³   = 5^{(5 - 3)} = 5²

Final result :

  400