The expressions which are equivalent to 6¹⁶ are
[tex](6^{8}) ^{2}[/tex]
[tex](6^{-2}) ^{\times -8}[/tex]
and [tex](6^{-4}) ^{\times -4}[/tex]
From the question, we are to determine which of the given expressions are equivalent to 6¹⁶
From one of the laws of indices, we have that
[tex]x^{y\times z} = (x^{y})^{z}[/tex]
The given expression, 6¹⁶, can be expressed as
[tex]6^{8\times 2}[/tex]
or
[tex]6^{-2\times -8}[/tex]
or
[tex]6^{-4\times -4}[/tex]
Then,
[tex]6^{8\times 2}= (6^{8}) ^{2}[/tex]
[tex]6^{-2\times -8}= (6^{-2}) ^{\times -8}[/tex]
[tex]6^{-4\times -4}= (6^{-4}) ^{\times -4}[/tex]
Hence, the expressions which are equivalent to 6¹⁶ are
[tex](6^{8}) ^{2}[/tex]
[tex](6^{-2}) ^{\times -8}[/tex]
and [tex](6^{-4}) ^{\times -4}[/tex]
Learn more on Equivalent expressions here: https://brainly.com/question/21643960
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