Question

fully simplify using only positive exponents.\\(\frac{4x^{4}y^{7}}{2x^{8}y^{7}}\\)

Explanation:

Step1: Simplify the coefficient

Simplify the fraction of the coefficients $\frac{4}{2}$.
$\frac{4}{2} = 2$

Step2: Simplify the \(x\)-terms using exponent rule

Use the exponent rule $\frac{a^m}{a^n}=a^{m - n}$ for the \(x\)-terms $\frac{x^4}{x^8}$.
$\frac{x^4}{x^8}=x^{4 - 8}=x^{- 4}$

Step3: Simplify the \(y\)-terms using exponent rule

Use the exponent rule $\frac{a^m}{a^n}=a^{m - n}$ for the \(y\)-terms $\frac{y^7}{y^7}$.
$\frac{y^7}{y^7}=y^{7 - 7}=y^{0}=1$ (since $a^0 = 1$ for $a
eq0$)

Step4: Combine the simplified terms

Multiply the simplified coefficient, \(x\)-term, and \(y\)-term together. Also, rewrite $x^{-4}$ as $\frac{1}{x^4}$ to have only positive exponents.
$2\times x^{-4}\times1 = 2\times\frac{1}{x^4}=\frac{2}{x^4}$

Answer:

$\frac{2}{x^4}$