Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "^-43" was replaced by "^(-43)".

Step  1  :

 1.1     10 = 2•5

(10)²⁰ = (2•5)²⁰ = 2²⁰ • 5²⁰

Equation at the end of step  1  :

  (5 • (10-43)) • (8 • (220•520))

Step  2  :

Raising to a Power :

 2.1    2³  multiplied by  2²⁰   = 2^{(3 + 20)} = 2²³

Equation at the end of step  2  :

  (5 • (10-43)) • (223•520)

Step  3  :

 3.1     10 = 2•5

(10)^-43 = (2•5)^(-43) = (2)^(-43) • (5)^(-43)

Equation at the end of step  3  :

  (5 • ((2)(-43)•(5)(-43))) • (223•520)

Step  4  :

Dividing exponents :

 4.1    5¹   divided by   5⁴³   = 5^{(1 - 43)} = 5^(-42) = ¹/_5⁴²

Equation at the end of step  4  :

      1    
  ————————— • (223•520)
  (243•542) 

Step  5  :

Dividing exponents :

 5.1    2²³   divided by   2⁴³   = 2^{(23 - 43)} = 2^(-20) = ¹/_2²⁰

Dividing exponents :

 5.2    5²⁰   divided by   5⁴²   = 5^{(20 - 42)} = 5^(-22) = ¹/_5²²

Final result :

      1                                       
  ————————— = 4.00000 • 10-22 
  (220•522)