Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "^-5" was replaced by "^(-5)".

(2): "1.5" was replaced by "(15/10)". 2 more similar replacement(s)

Step  1  :

 1.1     10 = 2•5

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

Equation at the end of step  1  :

   45        15
  (——•(1015))——•((2)(-5)•(5)(-5)))
   10(       10

Step  2  :

            3
 Simplify   —
            2

Equation at the end of step  2  :

   45              3
  (—— • (1015)) ÷ (— • ((2)(-5)•(5)(-5)))
   10              2

Step  3  :

Raising to a Power :

 3.1    2¹  multiplied by  2⁵   = 2^{(1 + 5)} = 2⁶

Equation at the end of step  3  :

   45                3   
  (—— • (1015)) ÷ ———————
   10             (26•55)

Step  4  :

 4.1     10 = 2•5

(10)¹⁵ = (2•5)¹⁵ = 2¹⁵ • 5¹⁵

Equation at the end of step  4  :

   45                   3   
  (—— • (215•515)) ÷ ———————
   10                (26•55)

Step  5  :

            9
 Simplify   —
            2

Equation at the end of step  5  :

  9                   3   
  — • (215•515)) ÷ ———————
  2                (26•55)

Step  6  :

Dividing exponents :

 6.1    2¹⁵   divided by   2¹   = 2^{(15 - 1)} = 2¹⁴

Equation at the end of step  6  :

  15)3 
  ———————
  (26•55)

Step  7  :

                              3   
 Divide  (32•214•515)  by  ———————
                           (26•55)

Multiplying exponents :

 7.1    2¹⁴  multiplied by  2⁶   = 2^{(14 + 6)} = 2²⁰

Multiplying exponents :

 7.2    5¹⁵  multiplied by  5⁵   = 5^{(15 + 5)} = 5²⁰

Dividing exponents :

 7.3    3²   divided by   3¹   = 3^{(2 - 1)} = 3¹ = 3

Final result :

  (3•220•520)