Answer:
2. [tex]-2x^{8}y^{18}[/tex]
Step-by-step explanation:
We have been given an expression [tex]\frac{10x^{6}y^{12}}{-5x^{-2}y^{-6}}[/tex] and we are asked to find equivalent expression to our given expression.
Using fraction rule [tex]\frac{a}{-b} =-\frac{a}{b}[/tex] we can write our expression as: [tex]-\frac{10x^{6}y^{12}}{5x^{-2}y^{-6}}[/tex].
Upon dividing 10 by 5 we will get,
[tex]-\frac{2x^{6}y^{12}}{x^{-2}y^{-6}}[/tex]
Upon using exponent property for quotient [tex](\frac{a^{m}}{a^{n}} =a^{(m-n)})[/tex] we will get,
[tex]-\frac{2x^{6}y^{12}}{x^{-2}y^{-6}}=-2x^{(6--2)}y^{(12--6)}[/tex]
[tex]-2x^{(6+2)}y^{(12+6)}[/tex]
[tex]-2x^{8}y^{18}[/tex]
Therefore, our expression simplifies as [tex]-2x^{8}y^{18}[/tex] and 2nd option is the correct choice.
