Answer:
[tex]-2a^{11}b^9[/tex]
Explanation:
Given the expression:
[tex]\frac{-10a^2b^4}{5a^{-9}b^{-5}}[/tex]
First, rewrite the fraction by separating the constants, and variables a and b.
[tex]\begin{gathered} \frac{-10a^2b^4}{5a^{-9}b^{-5}}=-\frac{10}{5}\times\frac{a^2}{a^{-9}}\times\frac{b^4}{b^{-5}} \\ =-2\times\frac{a^2}{a^{-9}}\times\frac{b^4}{b^{-5}} \end{gathered}[/tex]
Next, apply the division rule of exponents:
[tex]\frac{x^m}{x^n}=x^{m-n}[/tex]
So, we have:
[tex]\begin{gathered} =-2\times a^{2-(-9)}\times b^{4-(-5)} \\ =-2\times a^{2+9}\times b^{4+5} \\ =-2a^{11}b^9 \end{gathered}[/tex]
The simplified form of the expression without any negative exponent is:
[tex]-2a^{11}b^9[/tex]
