Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "^-3" was replaced by "^(-3)". 1 more similar replacement(s)

(2): "8.5" was replaced by "(85/10)".

Step  1  :

 1.1     10 = 2•5

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

Equation at the end of step  1  :

                  85
  (2 • (10-5)) • (—— • ((2)(-3)•(5)(-3)))
                  10

Step  2  :

            17
 Simplify   ——
            2 

Equation at the end of step  2  :

                  17
  (2 • (10-5)) • (—— • ((2)(-3)•(5)(-3)))
                  2 

Step  3  :

Raising to a Power :

 3.1    2¹  multiplied by  2³   = 2^{(1 + 3)} = 2⁴

Equation at the end of step  3  :

                  17 
  (2 • (10-5)) • ————
                 2000

Step  4  :

 4.1     10 = 2•5

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

Equation at the end of step  4  :

                             17 
  (2 • ((2)(-5)•(5)(-5))) • ————
                            2000

Step  5  :

Dividing exponents :

 5.1    2¹   divided by   2⁵   = 2^{(1 - 5)} = 2^(-4) = ¹/_2⁴

Equation at the end of step  5  :

     1       17 
  ——————— • ————
  (24•55)   2000

Step  6  :

Multiplying exponents :

 6.1    2⁴  multiplied by  2⁴   = 2^{(4 + 4)} = 2⁸

Multiplying exponents :

 6.2    5⁵  multiplied by  5³   = 5^{(5 + 3)} = 5⁸

Final result :

     17                                    
  ——————— = 1.70000 • 10-7 
  (28•58)