The second option is correct. The resulting expression when the indices is simplified according to the law of indices is [tex]\frac{5x^2}{y^5}\\[/tex]
Given the indices expression;
[tex]\dfrac{15x^4y^{-2}}{3x^2y^3}[/tex]
Using the following laws of indices to solve the problem:
[tex]a^n \times a^m = a^{n+m}\\a^n \div a^m = a^{n-m}\\[/tex]
From the given indices
[tex]\dfrac{15x^4y^{-2}}{3x^2y^3}\\=\frac{15}{3} \times \frac{x^4}{x^2} \times \frac{y^{-2}}{y^3}\\= 5 \times x^{4-2} \times y^{-2-3}\\=5\times x^2y^{-5} \\= 5x^2y^{-5[/tex]
This can also be expressed as:
[tex]=5x^2 \times \frac{1}{y^5}\\= \frac{5x^2}{y^5}\\[/tex]
Learn more here:
https://brainly.com/question/20298728
