Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "1.2" was replaced by "(12/10)". 2 more similar replacement(s)

Step  1  :

 1.1     10 = 2•5

(10)⁴ = (2•5)⁴ = 2⁴ • 5⁴

Equation at the end of step  1  :

   48       12
  (——•(106))——•(24•54))
   10(      10

Step  2  :

            6
 Simplify   —
            5

Equation at the end of step  2  :

   48             6
  (—— • (106)) ÷ (— • (24•54))
   10             5

Step  3  :

Multiplying exponents :

 3.1    2¹  multiplied by  2⁴   = 2^{(1 + 4)} = 2⁵

Raising to a Power :

 3.2    5⁴   divided by   5¹   = 5^{(4 - 1)} = 5³

Equation at the end of step  3  :

   48
  (—— • (106)) ÷ (25•3•53)
   10

Step  4  :

 4.1     10 = 2•5

(10)⁶ = (2•5)⁶ = 2⁶ • 5⁶

Equation at the end of step  4  :

   48
  (—— • (26•56)) ÷ (25•3•53)
   10

Step  5  :

            24
 Simplify   ——
            5 

Equation at the end of step  5  :

  24
  —— • (26•56)) ÷ (25•3•53)
  5 

Step  6  :

Multiplying exponents :

 6.1    2³  multiplied by  2⁶   = 2^{(3 + 6)} = 2⁹

Dividing exponents :

 6.2    5⁶   divided by   5¹   = 5^{(6 - 1)} = 5⁵

Equation at the end of step  6  :

Step  7  :

            (29•3•55)
 Simplify   —————————
            (25•3•53)

Dividing exponents :

 7.1    2⁹   divided by   2⁵   = 2^{(9 - 5)} = 2⁴

Canceling Out :

 7.2      Canceling out  3  as it appears on both sides of the fraction line

Dividing exponents :

 7.3    5⁵   divided by   5³   = 5^{(5 - 3)} = 5²

Final result :

  400