Answer
$\frac{10}{x^{8}z^{15}}$
Work Step by Step
We are given the expression $\frac{30x^{-7}yz^{-14}}{3xyz}$.
To simplify, we can separate like terms and then use the quotient rule, which holds that $\frac{a^{m}}{a^{n}}=a^{m-n}$ (where a is a nonzero real number, and m and n are integers).
$(\frac{30}{3})\times(x^{-7-1})\times(y^{1-1})\times(z^{-14-1})=10\times x^{-8}\times y^{0}\times z^{-15}$
Note that $y^{0}=1$.
$10\times x^{-8}\times z^{-15}$
To simplify this into only positive exponents, we know that $a^{-n}=\frac{1}{a^{n}}$ (where a is a nonzero real number and n is a positive integer).
$10\times x^{-8}\times z^{-15}=\frac{10}{x^{8}z^{15}}$
