Question

fully simplify using only positive exponents.\\(
\frac{4xy^{4}}{2x^{6}y^{2}}
\\)

Explanation:

Step1: Simplify the coefficients

Divide the coefficient 4 by 2: $\frac{4}{2} = 2$

Step2: Simplify the x - terms using exponent rule $a^m\div a^n=a^{m - n}$

For the x - terms, we have $x^1\div x^6=x^{1 - 6}=x^{-5}$. Since we want only positive exponents, $x^{-5}=\frac{1}{x^5}$

Step3: Simplify the y - terms using exponent rule $a^m\div a^n=a^{m - n}$

For the y - terms, we have $y^4\div y^2=y^{4 - 2}=y^{2}$

Step4: Combine the simplified terms

Multiply the simplified coefficient, x - term, and y - term together: $2\times\frac{1}{x^5}\times y^{2}=\frac{2y^{2}}{x^5}$

Answer:

$\frac{2y^{2}}{x^{5}}$