Applying the property of exponents, $\displaystyle a^{-n}=\frac{1}{a^n}$, where $n$ is a number

Applying the property of exponents, $\displaystyle a^{-n}=\frac{1}{a^n}$, where $n$ is a number

Divide fractions $\frac{1}{\frac{1}{x^{7}}e^{\left(x^6\right)}}$ with Keep, Change, Flip: $a\div \frac{b}{c}=\frac{a}{1}\div\frac{b}{c}=\frac{a}{1}\times\frac{c}{b}=\frac{a\cdot c}{b}$

Because polynomial functions ($x^{7}$) grow asymptotically slower than exponential functions ($e^{\left(x^6\right)}$), we can say that the expression $\lim_{x\to\infty }\left(\frac{x^{7}}{e^{\left(x^6\right)}}\right)$ tends to zero as $x$ goes to infinity