Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "^-7" was replaced by "^(-7)".

(2): "4.2" was replaced by "(42/10)".

Step  1  :

 1.1     10 = 2•5

(10)^-7 = (2•5)^(-7) = (2)^(-7) • (5)^(-7)

Equation at the end of step  1  :

    42
  ((—— • (103)) • 2) • ((2)(-7)•(5)(-7))
    10

Step  2  :

 2.1     10 = 2•5

(10)³ = (2•5)³ = 2³ • 5³

Equation at the end of step  2  :

    42
  ((—— • (23•53)) • 2) • ((2)(-7)•(5)(-7))
    10

Step  3  :

            21
 Simplify   ——
            5 

Equation at the end of step  3  :

    21
  ((—— • (23•53)) • 2) • ((2)(-7)•(5)(-7))
    5 

Step  4  :

Dividing exponents :

 4.1    5³   divided by   5¹   = 5^{(3 - 1)} = 5²

Equation at the end of step  4  :

  (4200 • 2) • ((2)(-7)•(5)(-7))

Step  5  :

Dividing exponents :

 5.1    2⁴   divided by   2⁷   = 2^{(4 - 7)} = 2^(-3) = ¹/_2³

Dividing exponents :

 5.2    5²   divided by   5⁷   = 5^{(2 - 7)} = 5^(-5) = ¹/_5⁵

Final result :

     21             
  ——————— = 0.00084 
  (23•55)