Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

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

(2): "2.5" was replaced by "(25/10)".

Step  1  :

 1.1     10 = 2•5

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

Equation at the end of step  1  :

                 25
  (4 • (102)) • (—— • ((2)(-3)•(5)(-3)))
                 10

Step  2  :

            5
 Simplify   —
            2

Equation at the end of step  2  :

                 5
  (4 • (102)) • (— • ((2)(-3)•(5)(-3)))
                 2

Step  3  :

Multiplying exponents :

 3.1    2¹  multiplied by  2³   = 2^{(1 + 3)} = 2⁴

Raising to a Power :

 3.2    5¹   divided by   5³   = 5^{(1 - 3)} = 5^(-2) = ¹/_5²

Equation at the end of step  3  :

                 1 
  (4 • (102)) • ———
                400

Step  4  :

 4.1     10 = 2•5

(10)² = (2•5)² = 2² • 5²

Equation at the end of step  4  :

                   1 
  (4 • (22•52)) • ———
                  400

Step  5  :

Multiplying exponents :

 5.1    2²  multiplied by  2²   = 2^{(2 + 2)} = 2⁴

Equation at the end of step  5  :

             1 
  (24•52) • ———
            400

Step  6  :

Canceling Out :

 6.1      Canceling out  2⁴ as it appears on both sides of the fraction line

Canceling Out :

 6.2      Canceling out  5² as it appears on both sides of the fraction line

Final result :

  1