Question - Simplifying Algebraic Expression with Exponents
Solution:
To simplify the expression given, we'll apply the rules of exponents and combine like terms. The expression is:\[ \frac{10x^{5n+4} + 125x^{5n+2}}{3x^{5n+3} - 20x^{5n+1}} \]Starting with the numerator:\[ 10x^{5n+4} + 125x^{5n+2} \]This expression cannot be simplified further because the terms are not like terms (they have different exponents).Now let's look at the denominator:\[ 3x^{5n+3} - 20x^{5n+1} \]Similarly, this expression cannot be simplified further because the terms are not like terms (they have different exponents).Since we cannot simplify the individual parts of the numerator or the denominator any further, we can only simplify if there's a common factor in both the numerator and the denominator.Given that the exponents in each term of the numerator are different from those in the denominator, there are no obvious factors that would cancel out.Therefore, the expression is already in its simplest form:\[ \frac{10x^{5n+4} + 125x^{5n+2}}{3x^{5n+3} - 20x^{5n+1}} \]
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