Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "9.1" was replaced by "(91/10)". 2 more similar replacement(s)

Step  1  :

 1.1     10 = 2•5

(10)³ = (2•5)³ = 2³ • 5³

Equation at the end of step  1  :

    27        91
  ((——•(104))•——)•(23•53)
    10        10

Step  2  :

            91
 Simplify   ——
            10

Equation at the end of step  2  :

    27            91
  ((—— • (104)) • ——) • (23•53)
    10            10

Step  3  :

 3.1     10 = 2•5

(10)⁴ = (2•5)⁴ = 2⁴ • 5⁴

Equation at the end of step  3  :

    27              91
  ((—— • (24•54)) • ——) • (23•53)
    10              10

Step  4  :

            27
 Simplify   ——
            10

Equation at the end of step  4  :

    27              91
  ((—— • (24•54)) • ——) • (23•53)
    10              10

Step  5  :

Dividing exponents :

 5.1    2⁴   divided by   2¹   = 2^{(4 - 1)} = 2³

Dividing exponents :

 5.2    5⁴   divided by   5¹   = 5^{(4 - 1)} = 5³

Equation at the end of step  5  :

                91
  ((33•23•53) • ——) • (23•53)
                10

Step  6  :

Dividing exponents :

 6.1    2³   divided by   2¹   = 2^{(3 - 1)} = 2²

Dividing exponents :

 6.2    5³   divided by   5¹   = 5^{(3 - 1)} = 5²

Equation at the end of step  6  :

  (33•22•52•7•13) • (23•53)

Step  7  :

Multiplying exponents :

 7.1    2²  multiplied by  2³   = 2^{(2 + 3)} = 2⁵

Multiplying exponents :

 7.2    5²  multiplied by  5³   = 5^{(2 + 3)} = 5⁵

Final result :

  (33•25•55•7•13)