Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

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

(2): "5.76" was replaced by "(576/100)". 2 more similar replacement(s)

Step  1  :

 1.1     10 = 2•5

(10)¹⁰ = (2•5)¹⁰ = 2¹⁰ • 5¹⁰

Equation at the end of step  1  :

   25          576
  (——•(10-3))•(———•(210•510))
   10          100

Step  2  :

            144
 Simplify   ———
            25 

Equation at the end of step  2  :

   25              144
  (—— • (10-3)) • (——— • (210•510))
   10              25 

Step  3  :

Multiplying exponents :

 3.1    2⁴  multiplied by  2¹⁰   = 2^{(4 + 10)} = 2¹⁴

Raising to a Power :

 3.2    5¹⁰   divided by   5²   = 5^{(10 - 2)} = 5⁸

Equation at the end of step  3  :

   25
  (—— • (10-3)) • (214•32•58)
   10

Step  4  :

 4.1     10 = 2•5

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

Equation at the end of step  4  :

   25
  (—— • ((2)(-3)•(5)(-3))) • (214•32•58)
   10

Step  5  :

            5
 Simplify   —
            2

Equation at the end of step  5  :

   5
  (— • ((2)(-3)•(5)(-3))) • (214•32•58)
   2

Step  6  :

Multiplying exponents :

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

Dividing exponents :

 6.2    5¹   divided by   5³   = 5^{(1 - 3)} = 5^(-2) = ¹/_5²

Equation at the end of step  6  :

   1 
  ——— • (214•32•58)
  400

Step  7  :

Dividing exponents :

 7.1    2¹⁴   divided by   2⁴   = 2^{(14 - 4)} = 2¹⁰

Dividing exponents :

 7.2    5⁸   divided by   5²   = 5^{(8 - 2)} = 5⁶

Final result :

  (210•32•56)