Option C: [tex](6^{-4})^{-4}[/tex]
Option D: [tex](6^{-2})^{-8}[/tex]
Option F: [tex](6^8)^2[/tex]
Solution:
Given expression: [tex]6^{16}[/tex]
To find which expression is equivalent to the given expression.
Let us solve this using exponent rule: [tex]\left(a^{b}\right)^{c}=a^{b c}[/tex]
Option A: [tex](6^{0})^{16}[/tex]
[tex](6^{0})^{16}=6^{0 \times 16}= 6^0[/tex]
It is not equivalent expression.
Option B: [tex](6^8)^8[/tex]
[tex](6^{8})^{8}=6^{8 \times 8}= 6^{64}[/tex]
It is not equivalent expression.
Option C: [tex](6^{-4})^{-4}[/tex]
[tex](6^{-4})^{-4}=6^{(-4 )\times (-4)}= 6^{16}[/tex]
It is equivalent expression for the given expression.
Option D: [tex](6^{-2})^{-8}[/tex]
[tex](6^{-2})^{-8}=6^{(-2) \times (-8)}= 6^{16}[/tex]
It is equivalent expression for the given expression.
Option E: [tex](6^{-1})^{16}[/tex]
[tex](6^{-1})^{16}=6^{(-1) \times 16}= 6^{-16}[/tex]
It is not equivalent expression.
Option F: [tex](6^8)^2[/tex]
[tex](6^{8})^{2}=6^{8 \times 2}= 6^{16}[/tex]
It is equivalent expression for the given expression.
Hence [tex](6^{-4})^{-4}, \ (6^{-2})^{-8}, \ (6^8)^2[/tex] are the equivalent expressions.
Option C, Option D and Option F are correct answers.
