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): "7.19" was replaced by "(719/100)".

Step  1  :

 1.1     10 = 2•5

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

Equation at the end of step  1  :

  )719
  ———— • ((2)(-3)•(5)(-3)))
  (100

Step  2  :

            719
 Simplify   ———
            100

Equation at the end of step  2  :

  )719
  ———— • ((2)(-3)•(5)(-3)))
  (100

Step  3  :

Multiplying exponents :

 3.1    2²  multiplied by  2³   = 2^{(2 + 3)} = 2⁵

Raising to a Power :

 3.2    5²  multiplied by  5³   = 5^{(2 + 3)} = 5⁵

Equation at the end of step  3  :

  ))719 
  ———————
  (25•55)

Step  4  :

 4.1     10 = 2•5

(10)^-4 = (2•5)^(-4) = (2)^(-4) • (5)^(-4)

Equation at the end of step  4  :

  ))719 
  ———————
  (25•55)

Step  5  :

Dividing exponents :

 5.1    2²   divided by   2⁴   = 2^{(2 - 4)} = 2^(-2) = ¹/_2²

Equation at the end of step  5  :

    1      719  
  ———— ÷ ———————
  2500   (25•55)

Step  6  :

           1         719  
 Divide  ————  by  ———————
         2500      (25•55)

 6.1    Dividing fractions

To divide fractions, write the divison as multiplication by the reciprocal of the divisor :

  1        719           1      (25•55)
————  ÷  ———————   =   ————  •  ———————
2500     (25•55)       2500       719  

Dividing exponents :

 6.2    2⁵   divided by   2²   = 2^{(5 - 2)} = 2³

Dividing exponents :

 6.3    5⁵   divided by   5⁴   = 5^{(5 - 4)} = 5¹ = 5

Final result :

   40           
  ——— = 0.05563 
  719