Question

simplify the expression using the properties of exponents. expand any numerical portion of your answer and only include positive exponents. \\(\frac{x^{6} \cdot x^{5}}{x^{-2}}\\)

Explanation:

Step1: Multiply exponents in numerator

Use the property \(a^m \cdot a^n = a^{m + n}\). For \(x^6 \cdot x^5\), we have \(x^{6 + 5}=x^{11}\). So the expression becomes \(\frac{x^{11}}{x^{-2}}\).

Step2: Divide exponents

Use the property \(\frac{a^m}{a^n}=a^{m - n}\). Here, \(m = 11\) and \(n=-2\), so \(x^{11-(-2)}=x^{11 + 2}=x^{13}\).

Answer:

\(x^{13}\)