Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "^-4" was replaced by "^(-4)".

(2): "2.8" was replaced by "(28/10)". 2 more similar replacement(s)

Step  1  :

 1.1     10 = 2•5

(10)⁶ = (2•5)⁶ = 2⁶ • 5⁶

Equation at the end of step  1  :

   14 28
  (——•——)•(26•56)
   10 10

Step  2  :

            14
 Simplify   ——
            5 

Equation at the end of step  2  :

   14   14
  (—— • ——) • (26•56)
   10   5 

Step  3  :

 3.1     10 = 2•5

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

Equation at the end of step  3  :

   14   14
  (—— • ——) • (26•56)
   10   5 

Step  4  :

            1         14
 Divide  ———————  by  ——
         (24•54)      5 

 4.1    Dividing fractions

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

   1        14          1         5
———————  ÷  ——   =   ———————  •  ——
(24•54)     5        (24•54)     14

Multiplying exponents :

 4.2    2⁴  multiplied by  2¹   = 2^{(4 + 1)} = 2⁵

Dividing exponents :

 4.3    5¹   divided by   5⁴   = 5^{(1 - 4)} = 5^(-3) = ¹/_5³

Equation at the end of step  4  :

   14       1    
  (—— • —————————) • (26•56)
   10   (25•53•7)

Step  5  :

            7
 Simplify   —
            5

Equation at the end of step  5  :

   7       1    
  (— • —————————) • (26•56)
   5   (25•53•7)

Step  6  :

Multiplying exponents :

 6.1    5¹  multiplied by  5³   = 5^{(1 + 3)} = 5⁴

Canceling Out :

 6.2      Canceling out  7  as it appears on both sides of the fraction line

Equation at the end of step  6  :

     1   
  ——————— • (26•56)
  (54•25)

Step  7  :

Dividing exponents :

 7.1    2⁶   divided by   2⁵   = 2^{(6 - 5)} = 2¹ = 2

Dividing exponents :

 7.2    5⁶   divided by   5⁴   = 5^{(6 - 4)} = 5²

Final result :

  50