Question

question
fully simplify using only positive exponents.
\\(\frac{24x^{3}y^{8}}{8x^{4}y^{6}}\\)
answer attempt 1 out of 5

Explanation:

Step1: Simplify the coefficient

Divide the coefficient 24 by 8: $\frac{24}{8} = 3$

Step2: Simplify the \(x\)-term

Use the exponent rule $\frac{x^m}{x^n}=x^{m - n}$. For \(x\): $\frac{x^3}{x^4}=x^{3 - 4}=x^{-1}=\frac{1}{x}$ (but we want positive exponents, so we'll handle this later with the \(y\)-term or keep it in mind)

Step3: Simplify the \(y\)-term

Use the exponent rule $\frac{y^m}{y^n}=y^{m - n}$. For \(y\): $\frac{y^8}{y^6}=y^{8 - 6}=y^{2}$

Step4: Combine and adjust for positive exponents

Now combine the coefficient, \(x\)-term, and \(y\)-term. We have $3\times\frac{1}{x}\times y^{2}=\frac{3y^{2}}{x}$

Answer:

$\frac{3y^{2}}{x}$