Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "^-3" was replaced by "^(-3)". 1 more similar replacement(s)

(2): "4.8" was replaced by "(48/10)".

Step  1  :

 1.1     10 = 2•5

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

Equation at the end of step  1  :

   48
  (—— • (10-8)) ÷ (3 • ((2)(-3)•(5)(-3)))
   10

Step  2  :

Equation at the end of step  2  :

   48               3 
  (—— • (10-8)) ÷ ————
   10             1000

Step  3  :

 3.1     10 = 2•5

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

Equation at the end of step  3  :

   48                          3 
  (—— • ((2)(-8)•(5)(-8))) ÷ ————
   10                        1000

Step  4  :

            24
 Simplify   ——
            5 

Equation at the end of step  4  :

  24                          3 
  —— • ((2)(-8)•(5)(-8))) ÷ ————
  5                         1000

Step  5  :

Multiplying exponents :

 5.1    5¹  multiplied by  5⁸   = 5^{(1 + 8)} = 5⁹

Dividing exponents :

 5.2    2³   divided by   2⁸   = 2^{(3 - 8)} = 2^(-5) = ¹/_2⁵

Equation at the end of step  5  :

     3        3 
  ——————— ÷ ————
  (59•25)   1000

Step  6  :

            3           3 
 Divide  ———————  by  ————
         (59•25)      1000

 6.1    Dividing fractions

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

   3          3           3        1000
———————  ÷  ————   =   ———————  •  ————
(59•25)     1000       (59•25)      3  

Dividing exponents :

 6.2    2³   divided by   2⁵   = 2^{(3 - 5)} = 2^(-2) = ¹/_2²

Dividing exponents :

 6.3    5³   divided by   5⁹   = 5^{(3 - 9)} = 5^(-6) = ¹/_5⁶

Final result :

     1              
  ——————— = 0.00002 
  (56•22)