Answer
\[\frac{-5{{y}^{8}}}{{{x}^{6}}}\].
Work Step by Step
Quotient rule:
When exponential expressions with same base are divided then subtract the exponent in the denominator with the exponent in the numerator of the common base:
\[\frac{{{a}^{m}}}{{{a}^{n}}}={{a}^{m-n}}\].
So,
\[\begin{align}
& \frac{30{{x}^{2}}{{y}^{5}}}{-6{{x}^{8}}{{y}^{-3}}}=-\frac{30}{6}\left( {{x}^{2-8}}{{y}^{5-\left( -3 \right)}} \right) \\
& =-5{{x}^{-6}}{{y}^{5+3}} \\
& =-5{{x}^{-6}}{{y}^{8}}
\end{align}\]
Negative exponent rule:
For any real number \[b\]other than zero and \[m\]a natural number \[{{b}^{-m}}=\frac{1}{{{b}^{m}}}\].
Here, \[x\ne 0\]. So,
\[-5{{x}^{-6}}{{y}^{8}}=\frac{-5{{y}^{8}}}{{{x}^{6}}}\]
So, \[\frac{30{{x}^{2}}{{y}^{5}}}{-6{{x}^{8}}{{y}^{-3}}}=\frac{-5{{y}^{8}}}{{{x}^{6}}}\].
