Problem 90 - College Algebra

Question

Perform the indicated operation or operations. $$ \frac{(5 x-3)^{6}}{(5 x-3)^{4}} $$

Step-by-Step Solution

Answer

The simplified form of \( \frac{(5x-3)^{6}}{(5x-3)^{4}} \) is \( (5x-3)^{2} \).

Step 1: Identify the Base and Exponents

The expression to be simplified is \( \frac{(5x-3)^{6}}{(5x-3)^{4}} \). In both the numerator and denominator, the base is the term (5x-3) and the exponents are 6 and 4 respectively.

Step 2: Apply the Law of Exponents

Apply the law of exponents for division, which states that when dividing two exponential expressions that have the same base, subtract the exponent of the denominator from the exponent of the numerator. This yields \( (5x-3)^{6-4} \).

Step 3: Simplify

By performing the subtraction in the exponent, the final simplified expression is \( (5x-3)^{2} \).