Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "^-5" was replaced by "^(-5)".

(2): "4.7" was replaced by "(47/10)".

Step  1  :

 1.1     10 = 2•5

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

Equation at the end of step  1  :

                 47
  (3 • (102)) • (—— • ((2)(-5)•(5)(-5)))
                 10

Step  2  :

            47
 Simplify   ——
            10

Equation at the end of step  2  :

                 47
  (3 • (102)) • (—— • ((2)(-5)•(5)(-5)))
                 10

Step  3  :

Multiplying exponents :

 3.1    2¹  multiplied by  2⁵   = 2^{(1 + 5)} = 2⁶

Raising to a Power :

 3.2    5¹  multiplied by  5⁵   = 5^{(1 + 5)} = 5⁶

Equation at the end of step  3  :

                   47  
  (3 • (102)) • ———————
                (26•56)

Step  4  :

 4.1     10 = 2•5

(10)² = (2•5)² = 2² • 5²

Equation at the end of step  4  :

                     47  
  (3 • (22•52)) • ———————
                  (26•56)

Step  5  :

Equation at the end of step  5  :

                 47  
  (3•22•52) • ———————
              (26•56)

Step  6  :

Dividing exponents :

 6.1    2²   divided by   2⁶   = 2^{(2 - 6)} = 2^(-4) = ¹/_2⁴

Dividing exponents :

 6.2    5²   divided by   5⁶   = 5^{(2 - 6)} = 5^(-4) = ¹/_5⁴

Final result :

    141             
  ——————— = 0.01410 
  (24•54)