Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "^-2" was replaced by "^(-2)". 1 more similar replacement(s)

Step  1  :

 1.1     10 = 2•5

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

Equation at the end of step  1  :

  (7 • (10-8)) • (5 • ((2)(-2)•(5)(-2)))

Step  2  :

Raising to a Power :

 2.1    5¹   divided by   5²   = 5^{(1 - 2)} = 5^(-1) = ¹/_5¹ = ¹/₅

Equation at the end of step  2  :

                  1
  (7 • (10-8)) • ——
                 20

Step  3  :

 3.1     10 = 2•5

(10)^-8 = (2•5)^(-8) = (2)^(-8) • (5)^(-8)

Equation at the end of step  3  :

                             1
  (7 • ((2)(-8)•(5)(-8))) • ——
                            20

Step  4  :

Equation at the end of step  4  :

     7       1
  ——————— • ——
  (28•58)   20

Step  5  :

Multiplying exponents :

 5.1    2⁸  multiplied by  2²   = 2^{(8 + 2)} = 2¹⁰

Multiplying exponents :

 5.2    5⁸  multiplied by  5¹   = 5^{(8 + 1)} = 5⁹

Final result :

      7                                     
  ———————— = 3.50000 • 10-9 
  (210•59)