Question - Simplifying an Algebraic Expression with Exponents and Division
mathfactor out common termsproperties of exponentssimplify algebraic expressionexponents and division rules
Solution:
To simplify the given expression, we follow the rules of exponents and division.The expression is:\[ \frac{10x^{5n+4} + 125x^{5n+2}}{3x^{5n+3} - 20x^{5n+1}} \]Let's break it down step by step:First, factor out the common factor of x in both numerator and denominator.In the numerator, the smallest power of x is $$x^{5n+2}$$, and in the denominator, the smallest power is $$x^{5n+1}$$. We factor these out from both parts:Numerator factor: $$x^{5n+2}$$ (leaving $$10x^2 + 125$$)Denominator factor: $$x^{5n+1}$$ (leaving $$3x^2 - 20$$)After factoring out, we have:\[ \frac{x^{5n+2}(10x^2 + 125)}{x^{5n+1}(3x^2 - 20)} \]Now we can simplify $$x^{5n+2}$$ and $$x^{5n+1}$$. Subtracting the exponents (using the properties of exponents), we get $$x^{5n+2 - (5n+1)} = x^{(5n+2) - 5n - 1} = x^1 = x$$.The simplified form of the expression is:\[ \frac{x(10x^2 + 125)}{3x^2 - 20} \]We cannot simplify any further without knowing the specific values for x. This is the simplified expression in terms of x and n.
CamTutor
In regards to math, we are professionals.
Get In Touch
Email: camtutor.ai@gmail.com