Question

ully simplify using only positive exponents.
\\(\frac{5x^{4}y^{6}}{5x^{2}y^{5}}\\)

Explanation:

Step1: Simplify the coefficient

The coefficient of the numerator is 5 and the coefficient of the denominator is 5. So, we divide 5 by 5.
$\frac{5}{5} = 1$

Step2: Simplify the \(x\)-terms

Using the rule of exponents $\frac{a^m}{a^n}=a^{m - n}$, for the \(x\)-terms, we have \(x^{4}\) in the numerator and \(x^{2}\) in the denominator.
So, $x^{4-2}=x^{2}$

Step3: Simplify the \(y\)-terms

Again, using the rule of exponents $\frac{a^m}{a^n}=a^{m - n}$, for the \(y\)-terms, we have \(y^{6}\) in the numerator and \(y^{5}\) in the denominator.
So, $y^{6 - 5}=y^{1}=y$

Step4: Combine the simplified terms

Multiply the simplified coefficient, \(x\)-term, and \(y\)-term together.
$1\times x^{2}\times y=x^{2}y$

Answer:

\(x^{2}y\)