Short Answer 
Javier made three key mistakes in his simplification process: he failed to raise the coefficient of 5 to the correct power, misrepresented the exponent of x as 4 instead of 3, and applied the wrong exponent rule by dividing rather than subtracting the exponents. Each error significantly affected the overall result and simplified expression.
Step 1: Identify the Missing Coefficient
Javier’s first mistake was that he failed to raise the coefficient to the appropriate power. When simplifying expressions, it’s crucial to follow the rules precisely, especially regarding coefficients. In this instance, the coefficient of 5 should have been raised to the power of 3, which impacts the overall result.
Step 2: Correct the Exponent of x
Secondly, Javier incorrectly recorded the exponent of x. Instead of writing it as x raised to the power of 3, he mistakenly noted it as x raised to the power of 4. This is significant because the exponent determines the growth and behavior of the expression, thus leading to an incorrect simplification.
Step 3: Apply the Correct Exponent Rule
Javier’s third mistake involved using the incorrect mathematical property to simplify the exponents. He divided the exponents instead of subtracting them as the exponent rule dictates. Correctly applying the formula a^m / a^n = a^(m-n) is essential to get the right outcome in simplifications involving exponents.