Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "^-6" was replaced by "^(-6)". 1 more similar replacement(s)

(2): "2.5" was replaced by "(25/10)". 2 more similar replacement(s)

Step  1  :

 1.1     10 = 2•5

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

Equation at the end of step  1  :

   25        25
  (——•(10-5))——•((2)(-6)•(5)(-6)))
   10(       10

Step  2  :

            5
 Simplify   —
            2

Equation at the end of step  2  :

   25              5
  (—— • (10-5)) ÷ (— • ((2)(-6)•(5)(-6)))
   10              2

Step  3  :

Multiplying exponents :

 3.1    2¹  multiplied by  2⁶   = 2^{(1 + 6)} = 2⁷

Raising to a Power :

 3.2    5¹   divided by   5⁶   = 5^{(1 - 6)} = 5^(-5) = ¹/_5⁵

Equation at the end of step  3  :

   25                1   
  (—— • (10-5)) ÷ ———————
   10             (27•55)

Step  4  :

 4.1     10 = 2•5

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

Equation at the end of step  4  :

   25                           1   
  (—— • ((2)(-5)•(5)(-5))) ÷ ———————
   10                        (27•55)

Step  5  :

            5
 Simplify   —
            2

Equation at the end of step  5  :

  5                           1   
  — • ((2)(-5)•(5)(-5))) ÷ ———————
  2                        (27•55)

Step  6  :

Multiplying exponents :

 6.1    2¹  multiplied by  2⁵   = 2^{(1 + 5)} = 2⁶

Dividing exponents :

 6.2    5¹   divided by   5⁵   = 5^{(1 - 5)} = 5^(-4) = ¹/_5⁴

Equation at the end of step  6  :

     1         1   
  ——————— ÷ ———————
  (26•54)   (27•55)

Step  7  :

            1            1   
 Divide  ———————  by  ———————
         (26•54)      (27•55)

 7.1    Dividing fractions

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

   1           1             1        (27•55)
———————  ÷  ———————   =   ———————  •  ———————
(26•54)     (27•55)       (26•54)        1   

Dividing exponents :

 7.2    2⁷   divided by   2⁶   = 2^{(7 - 6)} = 2¹ = 2

Dividing exponents :

 7.3    5⁵   divided by   5⁴   = 5^{(5 - 4)} = 5¹ = 5

Final result :

  10