Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "^-7" was replaced by "^(-7)". 1 more similar replacement(s)

(2): "2.65" was replaced by "(265/100)". 2 more similar replacement(s)

Step  1  :

 1.1     10 = 2•5

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

Equation at the end of step  1  :

   314 265
  (———•———)•((2)(-7)•(5)(-7))
   100 100

Step  2  :

            53
 Simplify   ——
            20

Equation at the end of step  2  :

   314   53
  (——— • ——) • ((2)(-7)•(5)(-7))
   100   20

Step  3  :

 3.1     10 = 2•5

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

Equation at the end of step  3  :

   314   53
  (——— • ——) • ((2)(-7)•(5)(-7))
   100   20

Step  4  :

            1         53
 Divide  ———————  by  ——
         (22•52)      20

 4.1    Dividing fractions

To divide fractions, write the divison as multiplication by the reciprocal of the divisor :

   1        53          1        20
———————  ÷  ——   =   ———————  •  ——
(22•52)     20       (22•52)     53

Canceling Out :

 4.2      Canceling out  2² as it appears on both sides of the fraction line

Dividing exponents :

 4.3    5¹   divided by   5²   = 5^{(1 - 2)} = 5^(-1) = ¹/_5¹ = ¹/₅

Equation at the end of step  4  :

   314    1 
  (——— • ———) • ((2)(-7)•(5)(-7))
   100   265

Step  5  :

            157
 Simplify   ———
            50 

Equation at the end of step  5  :

   157    1 
  (——— • ———) • ((2)(-7)•(5)(-7))
   50    265

Step  6  :

Multiplying exponents :

 6.1    2¹  multiplied by  2⁷   = 2^{(1 + 7)} = 2⁸

Multiplying exponents :

 6.2    5³  multiplied by  5⁷   = 5^{(3 + 7)} = 5¹⁰

Final result :

      157                                      
  ——————————— = 1.18491 • 10-9 
  (28•510•53)