Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

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

(2): "4.3" was replaced by "(43/10)".

Step  1  :

 1.1     10 = 2•5

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

Equation at the end of step  1  :

   43
  (—— • (10-3)) • (2 • ((2)(-2)•(5)(-2)))
   10

Step  2  :

Raising to a Power :

 2.1    2¹   divided by   2²   = 2^{(1 - 2)} = 2^(-1) = ¹/_2¹ = ¹/₂

Equation at the end of step  2  :

   43              1
  (—— • (10-3)) • ——
   10             50

Step  3  :

 3.1     10 = 2•5

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

Equation at the end of step  3  :

   43                         1
  (—— • ((2)(-3)•(5)(-3))) • ——
   10                        50

Step  4  :

            43
 Simplify   ——
            10

Equation at the end of step  4  :

   43                         1
  (—— • ((2)(-3)•(5)(-3))) • ——
   10                        50

Step  5  :

Multiplying exponents :

 5.1    2¹  multiplied by  2³   = 2^{(1 + 3)} = 2⁴

Multiplying exponents :

 5.2    5¹  multiplied by  5³   = 5^{(1 + 3)} = 5⁴

Equation at the end of step  5  :

     43      1
  ——————— • ——
  (24•54)   50

Step  6  :

Multiplying exponents :

 6.1    2⁴  multiplied by  2¹   = 2^{(4 + 1)} = 2⁵

Multiplying exponents :

 6.2    5⁴  multiplied by  5²   = 5^{(4 + 2)} = 5⁶

Final result :

     43             
  ——————— = 0.00009 
  (25•56)