Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "^-9" was replaced by "^(-9)". 1 more similar replacement(s)

(2): "1.8" was replaced by "(18/10)". 2 more similar replacement(s)

Step  1  :

 1.1     10 = 2•5

(10)^-9 = (2•5)^(-9) = (2)^(-9) • (5)^(-9)

Equation at the end of step  1  :

    56         18
  ((——•(10-6))•——)•((2)(-9)•(5)(-9))
    10         10

Step  2  :

            9
 Simplify   —
            5

Equation at the end of step  2  :

    56             9
  ((—— • (10-6)) • —) • ((2)(-9)•(5)(-9))
    10             5

Step  3  :

 3.1     10 = 2•5

(10)^-6 = (2•5)^(-6) = (2)^(-6) • (5)^(-6)

Equation at the end of step  3  :

    56                        9
  ((—— • ((2)(-6)•(5)(-6))) • —) • ((2)(-9)•(5)(-9))
    10                        5

Step  4  :

            28
 Simplify   ——
            5 

Equation at the end of step  4  :

    28                        9
  ((—— • ((2)(-6)•(5)(-6))) • —) • ((2)(-9)•(5)(-9))
    5                         5

Step  5  :

Multiplying exponents :

 5.1    5¹  multiplied by  5⁶   = 5^{(1 + 6)} = 5⁷

Dividing exponents :

 5.2    2²   divided by   2⁶   = 2^{(2 - 6)} = 2^(-4) = ¹/_2⁴

Equation at the end of step  5  :

      7      9
  (——————— • —) • ((2)(-9)•(5)(-9))
   (57•24)   5

Step  6  :

Multiplying exponents :

 6.1    5⁷  multiplied by  5¹   = 5^{(7 + 1)} = 5⁸

Equation at the end of step  6  :

     63  
  ——————— • ((2)(-9)•(5)(-9))
  (58•24)

Step  7  :

Multiplying exponents :

 7.1    5⁸  multiplied by  5⁹   = 5^{(8 + 9)} = 5¹⁷

Multiplying exponents :

 7.2    2⁴  multiplied by  2⁹   = 2^{(4 + 9)} = 2¹³

Final result :

      63                                      
  ————————— = 1.00800 • 10-14 
  (517•213)