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)". 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  :

    6         15
  ((—•(10-8))•——)•(24•54)
    1         10

Step  2  :

            3
 Simplify   —
            2

Equation at the end of step  2  :

    6             3
  ((— • (10-8)) • —) • (24•54)
    1             2

Step  3  :

 3.1     10 = 2•5

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

Equation at the end of step  3  :

    6                        3
  ((— • ((2)(-8)•(5)(-8))) • —) • (24•54)
    1                        2

Step  4  :

            6
 Simplify   —
            1

Equation at the end of step  4  :

                             3
  ((6 • ((2)(-8)•(5)(-8))) • —) • (24•54)
                             2

Step  5  :

Dividing exponents :

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

Equation at the end of step  5  :

      3      3
  (——————— • —) • (24•54)
   (27•58)   2

Step  6  :

Multiplying exponents :

 6.1    2⁷  multiplied by  2¹   = 2^{(7 + 1)} = 2⁸

Equation at the end of step  6  :

     9   
  ——————— • (24•54)
  (28•58)

Step  7  :

Dividing exponents :

 7.1    2⁴   divided by   2⁸   = 2^{(4 - 8)} = 2^(-4) = ¹/_2⁴

Dividing exponents :

 7.2    5⁴   divided by   5⁸   = 5^{(4 - 8)} = 5^(-4) = ¹/_5⁴

Final result :

     9              
  ——————— = 0.00090 
  (24•54)