Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

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

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

Step  1  :

 1.1     10 = 2•5

(10)² = (2•5)² = 2² • 5²

Equation at the end of step  1  :

   82          2
  (——•(10-3))•(—•(22•52))
   10          1

Step  2  :

            2
 Simplify   —
            1

Equation at the end of step  2  :

   82
  (—— • (10-3)) • (2 • (22•52))
   10

Step  3  :

Raising to a Power :

 3.1    2¹  multiplied by  2²   = 2^{(1 + 2)} = 2³

Equation at the end of step  3  :

   82
  (—— • (10-3)) • (23•52)
   10

Step  4  :

 4.1     10 = 2•5

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

Equation at the end of step  4  :

   82
  (—— • ((2)(-3)•(5)(-3))) • (23•52)
   10

Step  5  :

            41
 Simplify   ——
            5 

Equation at the end of step  5  :

   41
  (—— • ((2)(-3)•(5)(-3))) • (23•52)
   5 

Step  6  :

Multiplying exponents :

 6.1    5¹  multiplied by  5³   = 5^{(1 + 3)} = 5⁴

Equation at the end of step  6  :

   41 
  ———— • (23•52)
  5000

Step  7  :

Canceling Out :

 7.1      Canceling out  2³ as it appears on both sides of the fraction line

Dividing exponents :

 7.2    5²   divided by   5⁴   = 5^{(2 - 4)} = 5^(-2) = ¹/_5²

Final result :

  41           
  —— = 1.64000 
  25