Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

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

(2): "2.1" was replaced by "(21/10)".

Step  1  :

 1.1     10 = 2•5

(10)² = (2•5)² = 2² • 5²

Equation at the end of step  1  :

    21
  ((—— • (10-3)) • 2) • (22•52)
    10

Step  2  :

 2.1     10 = 2•5

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

Equation at the end of step  2  :

    21
  ((—— • ((2)(-3)•(5)(-3))) • 2) • (22•52)
    10

Step  3  :

            21
 Simplify   ——
            10

Equation at the end of step  3  :

    21
  ((—— • ((2)(-3)•(5)(-3))) • 2) • (22•52)
    10

Step  4  :

Multiplying exponents :

 4.1    2¹  multiplied by  2³   = 2^{(1 + 3)} = 2⁴

Multiplying exponents :

 4.2    5¹  multiplied by  5³   = 5^{(1 + 3)} = 5⁴

Equation at the end of step  4  :

      21  
  (——————— • 2) • (22•52)
   (24•54)

Step  5  :

Dividing exponents :

 5.1    2¹   divided by   2⁴   = 2^{(1 - 4)} = 2^(-3) = ¹/_2³

Equation at the end of step  5  :

   21 
  ———— • (22•52)
  5000

Step  6  :

Dividing exponents :

 6.1    2²   divided by   2³   = 2^{(2 - 3)} = 2^(-1) = ¹/_2¹ = ¹/₂

Dividing exponents :

 6.2    5²   divided by   5⁴   = 5^{(2 - 4)} = 5^(-2) = ¹/_5²

Final result :

  21           
  —— = 0.42000 
  50