To solve the expression [tex]\( \sqrt{x^4} - y^2 \)[/tex] when [tex]\( x = 3 \)[/tex] and [tex]\( y = -6 \)[/tex], follow these steps:
1. Square the value of [tex]\( x \)[/tex] since [tex]\( x^4 \)[/tex] is [tex]\( x \)[/tex] raised to the power of 4:
[tex]\[
(3)^4 = 81
\][/tex]
2. Find the square root of [tex]\( 81 \)[/tex]:
[tex]\[
\sqrt{81} = 9
\][/tex]
3. Square the value of [tex]\( y \)[/tex]:
[tex]\[
(-6)^2 = 36
\][/tex]
4. Subtract [tex]\( y^2 \)[/tex] from [tex]\( \sqrt{x^4} \)[/tex]:
[tex]\[
9 - 36 = -27
\][/tex]
Therefore, 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].
So, the correct answer is:
[tex]\[
-27
\][/tex]
