Question

Can you help me with this math question

Answer 1

-45/2 = -22.5

Explanation:

The applicable rules of exponents are ...

`(a^b)(a^c)=a^(b+c)\\\\\sqrt[n]{a^m}=a^(m)/(n)\\\\(1)/(a^b)=a^(-b)`

__

These rules let us rewrite the expression as ...

`\frac{3x^{(7)/(2)}y^(-4)}{\sqrt[4]{16x^2y^4}}=\frac{3}{16^{(1)/(4)}}\cdot x^{(7)/(2)-(2)/(4)}y^{-4-(4)/(4)}=(3)/(2)\cdot x^3y^(-5)`

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.