The resulting equivalent expression is [tex]\frac{3}{2}a^2b^{11}[/tex]
Given the expression
- [tex]\frac{-18a^{-2}b^5}{-12a^{-4}b^{-6}}[/tex]
To simplify, we will use the laws of indices as shown:
- [tex]a^m \times a^n = a^{m+n}\\\frac{a^m}{a^n} = a^{m-n}[/tex]
Applying this to the equation above will give:
[tex]=\frac{-18a^{-2}b^5}{-12a^{-4}b^{-6}}\\=\frac{18}{12}a^{-2-(-4)}b^{5-(-6)}\\=\frac{3}{2} }a^{-2+4}b^{5+6}\\ =\frac{3}{2}a^2b^{11}[/tex]
Hence the resulting equivalent expression is [tex]\frac{3}{2}a^2b^{11}[/tex]
Learn more on law of indices here: https://brainly.com/question/8952483
