Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "^-5" was replaced by "^(-5)".

(2): "1.3" was replaced by "(13/10)".

Step  1  :

 1.1     10 = 2•5

(10)² = (2•5)² = 2² • 5²

Equation at the end of step  1  :

   13
  (—— • (10-5)) • (6 • (22•52))
   10

Step  2  :

Raising to a Power :

 2.1    2¹  multiplied by  2²   = 2^{(1 + 2)} = 2³

Equation at the end of step  2  :

   13
  (—— • (10-5)) • (23•3•52)
   10

Step  3  :

 3.1     10 = 2•5

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

Equation at the end of step  3  :

   13
  (—— • ((2)(-5)•(5)(-5))) • (23•3•52)
   10

Step  4  :

            13
 Simplify   ——
            10

Equation at the end of step  4  :

   13
  (—— • ((2)(-5)•(5)(-5))) • (23•3•52)
   10

Step  5  :

Multiplying exponents :

 5.1    2¹  multiplied by  2⁵   = 2^{(1 + 5)} = 2⁶

Multiplying exponents :

 5.2    5¹  multiplied by  5⁵   = 5^{(1 + 5)} = 5⁶

Equation at the end of step  5  :

     13  
  ——————— • (23•3•52)
  (26•56)

Step  6  :

Dividing exponents :

 6.1    2³   divided by   2⁶   = 2^{(3 - 6)} = 2^(-3) = ¹/_2³

Dividing exponents :

 6.2    5²   divided by   5⁶   = 5^{(2 - 6)} = 5^(-4) = ¹/_5⁴

Final result :

   39            
  ———— = 0.00780 
  5000