Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

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

(2): "1.2" was replaced by "(12/10)". 2 more similar replacement(s)

Step  1  :

 1.1     10 = 2•5

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

Equation at the end of step  1  :

   34         12
  (——•(105))•(——•((2)(-3)•(5)(-3)))
   10         10

Step  2  :

            6
 Simplify   —
            5

Equation at the end of step  2  :

   34             6
  (—— • (105)) • (— • ((2)(-3)•(5)(-3)))
   10             5

Step  3  :

Multiplying exponents :

 3.1    5¹  multiplied by  5³   = 5^{(1 + 3)} = 5⁴

Raising to a Power :

 3.2    2¹   divided by   2³   = 2^{(1 - 3)} = 2^(-2) = ¹/_2²

Equation at the end of step  3  :

   34              3 
  (—— • (105)) • ————
   10            2500

Step  4  :

 4.1     10 = 2•5

(10)⁵ = (2•5)⁵ = 2⁵ • 5⁵

Equation at the end of step  4  :

   34                3 
  (—— • (25•55)) • ————
   10              2500

Step  5  :

            17
 Simplify   ——
            5 

Equation at the end of step  5  :

   17                3 
  (—— • (25•55)) • ————
   5               2500

Step  6  :

Dividing exponents :

 6.1    5⁵   divided by   5¹   = 5^{(5 - 1)} = 5⁴

Equation at the end of step  6  :

                 3 
  (17•25•54) • ————
               2500

Step  7  :

Dividing exponents :

 7.1    2⁵   divided by   2²   = 2^{(5 - 2)} = 2³

Canceling Out :

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

Final result :

  408