Question

use the quotient rule for exponents to simplify.
\\(
\frac{x^{8}y^{9}}{x^{2}y^{9}}
\\)
\\(
\frac{x^{8}y^{9}}{x^{2}y^{9}} = \square
\\)
(type your answer using exponential notation. use positive expo

Explanation:

Step1: Apply quotient rule to \(x\) terms

The quotient rule for exponents is \(\frac{a^m}{a^n}=a^{m - n}\). For the \(x\) terms, \(m = 8\), \(n = 2\), so \(\frac{x^8}{x^2}=x^{8 - 2}=x^6\).

Step2: Apply quotient rule to \(y\) terms

For the \(y\) terms, \(m = 9\), \(n = 9\), so \(\frac{y^9}{y^9}=y^{9 - 9}=y^0 = 1\) (since \(a^0 = 1\) for \(a
eq0\)).

Step3: Multiply the results

Multiply the results of the \(x\) and \(y\) terms: \(x^6\times1=x^6\).

Answer:

\(x^6\)