Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "^-8" was replaced by "^(-8)".

(2): "1.5" was replaced by "(15/10)".

Step  1  :

 1.1     10 = 2•5

(10)¹² = (2•5)¹² = 2¹² • 5¹²

Equation at the end of step  1  :

                  15
  (2 • (10-8)) • (—— • (212•512))
                  10

Step  2  :

            3
 Simplify   —
            2

Equation at the end of step  2  :

                  3
  (2 • (10-8)) • (— • (212•512))
                  2

Step  3  :

Raising to a Power :

 3.1    2¹²   divided by   2¹   = 2^{(12 - 1)} = 2¹¹

Equation at the end of step  3  :

  (2 • (10-8)) • (3•211•512)

Step  4  :

 4.1     10 = 2•5

(10)^-8 = (2•5)^(-8) = (2)^(-8) • (5)^(-8)

Equation at the end of step  4  :

  (2 • ((2)(-8)•(5)(-8))) • (3•211•512)

Step  5  :

Dividing exponents :

 5.1    2¹   divided by   2⁸   = 2^{(1 - 8)} = 2^(-7) = ¹/_2⁷

Equation at the end of step  5  :

     1   
  ——————— • (3•211•512)
  (27•58)

Step  6  :

Dividing exponents :

 6.1    2¹¹   divided by   2⁷   = 2^{(11 - 7)} = 2⁴

Dividing exponents :

 6.2    5¹²   divided by   5⁸   = 5^{(12 - 8)} = 5⁴

Final result :

  (3•24•54)