To evaluate the given expression [tex]\(\sqrt{x^4} - y^2\)[/tex] with [tex]\(x = 3\)[/tex] and [tex]\(y = -6\)[/tex], follow these steps:
1. Substitute the values of [tex]\(x\)[/tex] and [tex]\(y\)[/tex] into the expression:
[tex]\[
\sqrt{3^4} - (-6)^2
\][/tex]
2. Calculate [tex]\(3^4\)[/tex]:
[tex]\[
3^4 = 3 \times 3 \times 3 \times 3 = 81
\][/tex]
3. Find the square root of 81:
[tex]\[
\sqrt{81} = 9
\][/tex]
4. Calculate [tex]\((-6)^2\)[/tex]:
[tex]\[
(-6)^2 = (-6) \times (-6) = 36
\][/tex]
5. Subtract [tex]\(36\)[/tex] from [tex]\(9\)[/tex]:
[tex]\[
9 - 36 = -27
\][/tex]
Thus, the value of the expression [tex]\(\sqrt{x^4} - y^2\)[/tex] when [tex]\(x = 3\)[/tex] and [tex]\(y = -6\)[/tex] is [tex]\(-27\)[/tex].
The correct answer is:
[tex]\[
-27
\][/tex]
