Which expression is equivalent to 18^2y^5 (3xy)^2for all values for `x` and `y` where the expression is defined?
To simplify the expression, we can apply the power rule, which states that (a^m)^n is equal to a^(m * n).
So, let's simplify the expression step by step:
18^2y^5 = (18^2)(y^5) = 324y^5
Now, let's simplify (3xy)^2 using the power rule:
(3xy)^2 = (3^2)(x^2)(y^2) = 9x^2y^2
Therefore, the expression 18^2y^5 (3xy)^2 is equivalent to:
324y^5 * 9x^2y^2
Finally, we can multiply the coefficients together:
324 * 9 = 2916
And multiply the variables together:
y^5 * y^2 = y^(5 + 2) = y^7
x^2 remains the same.
So, the final expression is:
2916x^2y^7