Further practice multiplying and simplifying radical expressions involving higher-order roots and variables.

ⓐ $(2\sqrt{6y^4})(12\sqrt{30y})$: Multiply the coefficients and radicands: $(2\sqrt{6y^4})(12\sqrt{30y}) = 24\sqrt{180y^5}$ Extract the largest perfect square factor ($36y^4$): $24\sqrt{36y^4 \cdot 5y} = 24\sqrt{36y^4} \cdot \sqrt{5y}$ Simplify the perfect square and multiply: $24 \cdot 6y^2\sqrt{5y} = 144y^2\sqrt{5y}$

ⓑ $(-4\sqrt[4]{9a^3})(3\sqrt[4]{27a^2})$: Multiply the coefficients and radicands: $(-4\sqrt[4]{9a^3})(3\sqrt[4]{27a^2}) = -12\sqrt[4]{243a^5}$ Extract the largest perfect fourth power factor ($81a^4$): $-12\sqrt[4]{81a^4 \cdot 3a} = -12\sqrt[4]{81a^4} \cdot \sqrt[4]{3a}$ Simplify and multiply: $-12 \cdot 3a\sqrt[4]{3a} = -36a\sqrt[4]{3a}$