Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

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

(2): "3.2" was replaced by "(32/10)".

Step  1  :

 1.1     10 = 2•5

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

Equation at the end of step  1  :

                 32
  (2 • (102)) • (—— • ((2)(-5)•(5)(-5)))
                 10

Step  2  :

            16
 Simplify   ——
            5 

Equation at the end of step  2  :

                 16
  (2 • (102)) • (—— • ((2)(-5)•(5)(-5)))
                 5 

Step  3  :

Multiplying exponents :

 3.1    5¹  multiplied by  5⁵   = 5^{(1 + 5)} = 5⁶

Raising to a Power :

 3.2    2⁴   divided by   2⁵   = 2^{(4 - 5)} = 2^(-1) = ¹/_2¹ = ¹/₂

Equation at the end of step  3  :

                   1  
  (2 • (102)) • ——————
                (56•2)

Step  4  :

 4.1     10 = 2•5

(10)² = (2•5)² = 2² • 5²

Equation at the end of step  4  :

                     1  
  (2 • (22•52)) • ——————
                  (56•2)

Step  5  :

Multiplying exponents :

 5.1    2¹  multiplied by  2²   = 2^{(1 + 2)} = 2³

Equation at the end of step  5  :

               1  
  (23•52) • ——————
            (56•2)

Step  6  :

Dividing exponents :

 6.1    2³   divided by   2¹   = 2^{(3 - 1)} = 2²

Dividing exponents :

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

Final result :

   4            
  ——— = 0.00640 
  625