Answer:
[tex]\frac{1}{5x^{8}y^{13}}[/tex]
Step-by-step explanation:
[tex]\frac{3x^{-6}y^{-3}}{15x^2y^{10}}[/tex]
To find out equivalent expression we need to simplify it
[tex]\frac{3}{15} =\frac{1}{5}[/tex] divided 3 on both sides
To simplify variables , use exponential property
[tex]\frac{a^m}{a^n} =a^{m-n}[/tex]
[tex]\frac{x^{-6}}{x^2} =x^{-6-2}=x^{-8}[/tex]
[tex]\frac{y^{-3}}{y^{10}} =y^{-3-10}=x^{-13}[/tex]
Our expression becomes
[tex]\frac{x^{-8}y^{-13}}{5}[/tex]
To remove negative exponent we move the variable with exponent to the denominator
[tex]\frac{1}{5x^{8}y^{13}}[/tex]
