Sure, let's find the value of each expression given [tex]\( x = -1 \)[/tex].
### Part (a)
Expression: [tex]\( \sqrt{-16x} \)[/tex]
First, substitute [tex]\( x = -1 \)[/tex] into the expression:
[tex]\[ -16x = -16(-1) = 16 \][/tex]
So the expression becomes:
[tex]\[ \sqrt{16} = 4 \][/tex]
Hence, the value of [tex]\( \sqrt{-16x} \)[/tex] when [tex]\( x = -1 \)[/tex] is [tex]\( \boxed{4} \)[/tex].
### Part (b)
Expression: [tex]\( \sqrt[3]{16 + 8x} \)[/tex]
First, substitute [tex]\( x = -1 \)[/tex] into the expression:
[tex]\[ 16 + 8x = 16 + 8(-1) = 16 - 8 = 8 \][/tex]
So the expression becomes:
[tex]\[ \sqrt[3]{8} = 2 \][/tex]
Hence, the value of [tex]\( \sqrt[3]{16 + 8x} \)[/tex] when [tex]\( x = -1 \)[/tex] is [tex]\( \boxed{2} \)[/tex].
### Part (c)
Expression: [tex]\( 2(\sqrt{12x - 16x})^3 \)[/tex]
First, let's combine the terms inside the square root:
[tex]\[ 12x - 16x = (12 - 16)x = -4x \][/tex]
Substitute [tex]\( x = -1 \)[/tex]:
[tex]\[ -4x = -4(-1) = 4 \][/tex]
So the expression becomes:
[tex]\[ 2(\sqrt{4})^3 = 2(2)^3 = 2 \times 8 = 16 \][/tex]
Hence, the value of [tex]\( 2(\sqrt{12x - 16x})^3 \)[/tex] when [tex]\( x = -1 \)[/tex] is [tex]\( \boxed{16} \)[/tex].
In summary:
- The value of [tex]\( \sqrt{-16x} \)[/tex] is [tex]\( 4 \)[/tex].
- The value of [tex]\( \sqrt[3]{16 + 8x} \)[/tex] is [tex]\( 2 \)[/tex].
- The value of [tex]\( 2(\sqrt{12x - 16x})^3 \)[/tex] is [tex]\( 16 \)[/tex].
