To find the value of the expression [tex]\( \sqrt{x^4} - y^2 \)[/tex] given [tex]\( x = 3 \)[/tex] and [tex]\( y = -6 \)[/tex], we proceed step-by-step as follows:
1. Calculate [tex]\( x^4 \)[/tex]:
[tex]\[ x^4 = 3^4 = 81 \][/tex]
2. Find the square root of [tex]\( x^4 \)[/tex]:
[tex]\[ \sqrt{x^4} = \sqrt{81} = 9 \][/tex]
3. Calculate [tex]\( y^2 \)[/tex]:
[tex]\[ y^2 = (-6)^2 = 36 \][/tex]
4. Compute the value of the expression [tex]\( \sqrt{x^4} - y^2 \)[/tex]:
[tex]\[ \sqrt{x^4} - y^2 = 9 - 36 = -27 \][/tex]
Therefore, the value of the expression when [tex]\( x = 3 \)[/tex] and [tex]\( y = -6 \)[/tex] is [tex]\( -27 \)[/tex].
