Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "^-3" was replaced by "^(-3)".

(2): "3.14" was replaced by "(314/100)".

Step  1  :

 1.1     10 = 2•5

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

Equation at the end of step  1  :

        314
  (15 • ———) • ((10 • ((2)(-3)•(5)(-3)))2)
        100

Step  2  :

Dividing exponents :

 2.1    2¹   divided by   2³   = 2^{(1 - 3)} = 2^(-2) = ¹/_2²

Raising to a Power :

 2.2    5¹   divided by   5³   = 5^{(1 - 3)} = 5^(-2) = ¹/_5²

Equation at the end of step  2  :

        314      1 
  (15 • ———) • (———)2)
        100     100

Step  3  :

 3.1     100 = 2²•5² (100)² = (2²•5²)² = 2⁴ • 5⁴

Equation at the end of step  3  :

        314       1   
  (15 • ———) • ———————
        100    (24•54)

Step  4  :

            157
 Simplify   ———
            50 

Equation at the end of step  4  :

        157       1   
  (15 • ———) • ———————
        50     (24•54)

Step  5  :

Multiplying exponents :

 5.1    2¹  multiplied by  2⁴   = 2^{(1 + 4)} = 2⁵

Multiplying exponents :

 5.2    5¹  multiplied by  5⁴   = 5^{(1 + 4)} = 5⁵

Final result :

    471             
  ——————— = 0.00471 
  (25•55)