Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "^-4" was replaced by "^(-4)". 1 more similar replacement(s)

(2): "9.4" was replaced by "(94/10)". 2 more similar replacement(s)

Step  1  :

 1.1     10 = 2•5

(10)^-4 = (2•5)^(-4) = (2)^(-4) • (5)^(-4)

Equation at the end of step  1  :

   401 94
  (———•——)•((2)(-4)•(5)(-4))
   100 10

Step  2  :

            47
 Simplify   ——
            5 

Equation at the end of step  2  :

   401   47
  (——— • ——) • ((2)(-4)•(5)(-4))
   100   5 

Step  3  :

 3.1     10 = 2•5

(10)^-3 = (2•5)^(-3) = (2)^(-3) • (5)^(-3)

Equation at the end of step  3  :

   401   47
  (——— • ——) • ((2)(-4)•(5)(-4))
   100   5 

Step  4  :

            1         47
 Divide  ———————  by  ——
         (23•53)      5 

 4.1    Dividing fractions

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

   1        47          1         5
———————  ÷  ——   =   ———————  •  ——
(23•53)     5        (23•53)     47

Dividing exponents :

 4.2    5¹   divided by   5³   = 5^{(1 - 3)} = 5^(-2) = ¹/_5²

Equation at the end of step  4  :

   401     1 
  (——— • ————) • ((2)(-4)•(5)(-4))
   100   9400

Step  5  :

            401
 Simplify   ———
            100

Equation at the end of step  5  :

   401     1 
  (——— • ————) • ((2)(-4)•(5)(-4))
   100   9400

Step  6  :

Multiplying exponents :

 6.1    2⁵  multiplied by  2⁴   = 2^{(5 + 4)} = 2⁹

Multiplying exponents :

 6.2    5⁴  multiplied by  5⁴   = 5^{(4 + 4)} = 5⁸

Final result :

      401                                     
  —————————— = 4.26596 • 10-8 
  (29•58•47)