Question

Which expression is equivalent to (36x ^ 4 * y ^ 5)/((3xy) ^ 2) defined? for all values of x and y where the expression is
Q
J 6x ^ 3 * y ^ 4
Η 4x ^ 2 * y ^ 3
F 12x ^ 3 * y ^ 4
G 27x ^ 2 * y ^ 3

Answer 1

To simplify the given expression \((36x^4y^5) / ((3xy)^2)\), we first simplify the denominator \((3xy)^2\):

\[
(3xy)^2 = (3^2)(x^2)(y^2) = 9x^2y^2
\]

Now we can rewrite the original expression:

\[
\frac{36x^4y^5}{9x^2y^2}
\]

Next, we simplify the fraction by dividing both the numerator and the denominator by their common factors:

1. **Numerical Coefficient:**
\[
\frac{36}{9} = 4
\]

2. **For \(x\) terms:**
\[
\frac{x^4}{x^2} = x^{4-2} = x^2
\]

3. **For \(y\) terms:**
\[
\frac{y^5}{y^2} = y^{5-2} = y^3
\]

Now, putting it all together, we have:

\[
\frac{36x^4y^5}{9x^2y^2} = 4x^2y^3
\]

Thus, the simplified expression is:

\[
4x^2y^3
\]

So the expression \( (36x^4 y^5) / ((3xy)^2) \) simplifies to **\( 4x^2y^3 \)**, which corresponds to option **Η**.