Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "^-3" was replaced by "^(-3)".

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

Step  1  :

 1.1     10 = 2•5

(10)² = (2•5)² = 2² • 5²

Equation at the end of step  1  :

   49          28
  (——•(10-3))•(——•(22•52))
   10          10

Step  2  :

            14
 Simplify   ——
            5 

Equation at the end of step  2  :

   49              14
  (—— • (10-3)) • (—— • (22•52))
   10              5 

Step  3  :

Multiplying exponents :

 3.1    2¹  multiplied by  2²   = 2^{(1 + 2)} = 2³

Raising to a Power :

 3.2    5²   divided by   5¹   = 5^{(2 - 1)} = 5¹ = 5

Equation at the end of step  3  :

   49
  (—— • (10-3)) • 280
   10

Step  4  :

 4.1     10 = 2•5

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

Equation at the end of step  4  :

   49
  (—— • ((2)(-3)•(5)(-3))) • 280
   10

Step  5  :

            49
 Simplify   ——
            10

Equation at the end of step  5  :

   49
  (—— • ((2)(-3)•(5)(-3))) • 280
   10

Step  6  :

Multiplying exponents :

 6.1    2¹  multiplied by  2³   = 2^{(1 + 3)} = 2⁴

Multiplying exponents :

 6.2    5¹  multiplied by  5³   = 5^{(1 + 3)} = 5⁴

Equation at the end of step  6  :

     49  
  ——————— • 280
  (24•54)

Step  7  :

Dividing exponents :

 7.1    2³   divided by   2⁴   = 2^{(3 - 4)} = 2^(-1) = ¹/_2¹ = ¹/₂

Dividing exponents :

 7.2    5¹   divided by   5⁴   = 5^{(1 - 4)} = 5^(-3) = ¹/_5³

Final result :

  343           
  ——— = 1.37200 
  250