Answer:
-45/2 = -22.5
Step-by-step explanation:
The applicable rules of exponents are ...
[tex](a^b)(a^c)=a^{b+c}\\\\\sqrt[n]{a^m}=a^\frac{m}{n}\\\\\dfrac{1}{a^b}=a^{-b}[/tex]
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These rules let us rewrite the expression as ...
[tex]\dfrac{3x^{\frac{7}{2}}y^{-4}}{\sqrt[4]{16x^2y^4}}=\dfrac{3}{16^{\frac{1}{4}}}\cdot x^{\frac{7}{2}-\frac{2}{4}}y^{-4-\frac{4}{4}}=\dfrac{3}{2}\cdot x^3y^{-5}[/tex]
Now, we know the values of a, b, c:
a = 3/2, b = 3, c = -5
Their product is (3/2)(3)(-5) = -45/2 = -22.5.
