Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "^-2" was replaced by "^(-2)".

(2): "2.3" was replaced by "(23/10)". 2 more similar replacement(s)

Step  1  :

 1.1     10 = 2•5

(10)⁴ = (2•5)⁴ = 2⁴ • 5⁴

Equation at the end of step  1  :

   15          23
  (——•(10-2))•(——•(24•54))
   10          10

Step  2  :

            23
 Simplify   ——
            10

Equation at the end of step  2  :

   15              23
  (—— • (10-2)) • (—— • (24•54))
   10              10

Step  3  :

Dividing exponents :

 3.1    2⁴   divided by   2¹   = 2^{(4 - 1)} = 2³

Raising to a Power :

 3.2    5⁴   divided by   5¹   = 5^{(4 - 1)} = 5³

Equation at the end of step  3  :

   15
  (—— • (10-2)) • (23•23•53)
   10

Step  4  :

 4.1     10 = 2•5

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

Equation at the end of step  4  :

   15
  (—— • ((2)(-2)•(5)(-2))) • (23•23•53)
   10

Step  5  :

            3
 Simplify   —
            2

Equation at the end of step  5  :

   3
  (— • ((2)(-2)•(5)(-2))) • (23•23•53)
   2

Step  6  :

Multiplying exponents :

 6.1    2¹  multiplied by  2²   = 2^{(1 + 2)} = 2³

Equation at the end of step  6  :

   3 
  ——— • (23•23•53)
  200

Step  7  :

Canceling Out :

 7.1      Canceling out  2³ as it appears on both sides of the fraction line

Dividing exponents :

 7.2    5³   divided by   5²   = 5^{(3 - 2)} = 5¹ = 5

Final result :

  345