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)

(2): "0.7" was replaced by "(7/10)". 2 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  :

    4           7
  (——•(10-6))•(——•((2)(-2)•(5)(-2)))
   10          10

Step  2  :

             7
 Simplify   ——
            10

Equation at the end of step  2  :

    4               7
  (—— • (10-6)) • (—— • ((2)(-2)•(5)(-2)))
   10              10

Step  3  :

Multiplying exponents :

 3.1    2¹  multiplied by  2²   = 2^{(1 + 2)} = 2³

Raising to a Power :

 3.2    5¹  multiplied by  5²   = 5^{(1 + 2)} = 5³

Equation at the end of step  3  :

    4               7 
  (—— • (10-6)) • ————
   10             1000

Step  4  :

 4.1     10 = 2•5

(10)^-6 = (2•5)^(-6) = (2)^(-6) • (5)^(-6)

Equation at the end of step  4  :

    4                          7 
  (—— • ((2)(-6)•(5)(-6))) • ————
   10                        1000

Step  5  :

            2
 Simplify   —
            5

Equation at the end of step  5  :

   2                          7 
  (— • ((2)(-6)•(5)(-6))) • ————
   5                        1000

Step  6  :

Multiplying exponents :

 6.1    5¹  multiplied by  5⁶   = 5^{(1 + 6)} = 5⁷

Dividing exponents :

 6.2    2¹   divided by   2⁶   = 2^{(1 - 6)} = 2^(-5) = ¹/_2⁵

Equation at the end of step  6  :

     1        7 
  ——————— • ————
  (57•25)   1000

Step  7  :

Multiplying exponents :

 7.1    5⁷  multiplied by  5³   = 5^{(7 + 3)} = 5¹⁰

Multiplying exponents :

 7.2    2⁵  multiplied by  2³   = 2^{(5 + 3)} = 2⁸

Final result :

      7                                     
  ———————— = 2.80000 • 10-9 
  (510•28)