Let's evaluate the expression [tex]\(\sqrt{x^4} - y^2\)[/tex] step by step given the values [tex]\(x = 3\)[/tex] and [tex]\(y = -6\)[/tex].
1. Calculate [tex]\(x^4\)[/tex]:
[tex]\[
x^4 = 3^4 = 81
\][/tex]
2. Calculate [tex]\(\sqrt{x^4}\)[/tex]:
[tex]\[
\sqrt{x^4} = \sqrt{81} = 9
\][/tex]
3. Calculate [tex]\(y^2\)[/tex]:
[tex]\[
y^2 = (-6)^2 = 36
\][/tex]
4. Substitute these values into the expression [tex]\(\sqrt{x^4} - y^2\)[/tex]:
[tex]\[
\sqrt{81} - 36 = 9 - 36 = -27
\][/tex]
So 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].
[tex]\[
\boxed{-27}
\][/tex]
