[tex]16x^{12}y^8 =2^4\cdot (x^3)^4\cdot (y^2)^4 = \red{\boxed{(2x^3y^2)^4}}[/tex]
[tex]\dfrac{1}{27}a^9b^6=\Big(\dfrac{1}{3}\Big)^3\cdot (a^3)^3\cdot (b^2)^3=\red{\boxed{\Big(\dfrac{1}{3}a^3b^2\Big)^3}}[/tex]
[tex]\dfrac{x^5}{32y^{10}}=\dfrac{x^5}{2^5(y^2)^5}= \red{\boxed{\Big( \dfrac{x}{2y^2} \Big)^5 }}[/tex]
[tex]125a^{15}b^3=5^3\cdot (a^5)^3 \cdot b^3=\red{\boxed{(5a^5b)^3}}[/tex]