Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "^-9" was replaced by "^(-9)".

(2): "7.35" was replaced by "(735/100)".

Step  1  :

 1.1     10 = 2•5

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

Equation at the end of step  1  :

    735
  ((——— • (105)) • 4) • ((2)(-9)•(5)(-9))
    100

Step  2  :

 2.1     10 = 2•5

(10)⁵ = (2•5)⁵ = 2⁵ • 5⁵

Equation at the end of step  2  :

    735
  ((——— • (25•55)) • 4) • ((2)(-9)•(5)(-9))
    100

Step  3  :

            147
 Simplify   ———
            20 

Equation at the end of step  3  :

    147
  ((——— • (25•55)) • 4) • ((2)(-9)•(5)(-9))
    20 

Step  4  :

Dividing exponents :

 4.1    2⁵   divided by   2²   = 2^{(5 - 2)} = 2³

Dividing exponents :

 4.2    5⁵   divided by   5¹   = 5^{(5 - 1)} = 5⁴

Equation at the end of step  4  :

  ((3•72•23•54) • 4) • ((2)(-9)•(5)(-9))

Step  5  :

Multiplying exponents :

 5.1    2³  multiplied by  2²   = 2^{(3 + 2)} = 2⁵

Equation at the end of step  5  :

  (3•72•25•54) • ((2)(-9)•(5)(-9))

Step  6  :

Dividing exponents :

 6.1    2⁵   divided by   2⁹   = 2^{(5 - 9)} = 2^(-4) = ¹/_2⁴

Dividing exponents :

 6.2    5⁴   divided by   5⁹   = 5^{(4 - 9)} = 5^(-5) = ¹/_5⁵

Final result :

    147             
  ——————— = 0.00294 
  (24•55)