Problem 90 - College Algebra Essentials

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 the given expression is \((5x - 3)^2 \).

Step 1: Identify the Bases and the Exponents

In the given expression, the base is \((5x - 3)\) and the exponents are 6 for the numerator and 4 for the denominator.

Step 2: Apply the Law of Exponents

According to the law of exponents, to divide terms with same base, subtract the exponent of the divisor from the exponent of the dividend. Therefore, the expression can be rewritten as \((5x - 3)^{6-4} = (5x - 3)^2 \).

Step 3: Simplification

Since we cannot simplify it further, \((5x - 3)^2 \) is the final answer.