Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

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

(2): "2.7" was replaced by "(27/10)". 2 more similar replacement(s)

Step  1  :

 1.1     10 = 2•5

(10)⁵ = (2•5)⁵ = 2⁵ • 5⁵

Equation at the end of step  1  :

   12          27
  (——•(10-3))•(——•(25•55))
   10          10

Step  2  :

            27
 Simplify   ——
            10

Equation at the end of step  2  :

   12              27
  (—— • (10-3)) • (—— • (25•55))
   10              10

Step  3  :

Dividing exponents :

 3.1    2⁵   divided by   2¹   = 2^{(5 - 1)} = 2⁴

Raising to a Power :

 3.2    5⁵   divided by   5¹   = 5^{(5 - 1)} = 5⁴

Equation at the end of step  3  :

   12
  (—— • (10-3)) • (33•24•54)
   10

Step  4  :

 4.1     10 = 2•5

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

Equation at the end of step  4  :

   12
  (—— • ((2)(-3)•(5)(-3))) • (33•24•54)
   10

Step  5  :

            6
 Simplify   —
            5

Equation at the end of step  5  :

   6
  (— • ((2)(-3)•(5)(-3))) • (33•24•54)
   5

Step  6  :

Multiplying exponents :

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

Dividing exponents :

 6.2    2¹   divided by   2³   = 2^{(1 - 3)} = 2^(-2) = ¹/_2²

Equation at the end of step  6  :

    3 
  ———— • (33•24•54)
  2500

Step  7  :

Multiplying exponents :

 7.1    3¹  multiplied by  3³   = 3^{(1 + 3)} = 3⁴

Dividing exponents :

 7.2    2⁴   divided by   2²   = 2^{(4 - 2)} = 2²

Canceling Out :

 7.3      Canceling out  5⁴ as it appears on both sides of the fraction line

Final result :

  324