The expression given to us is: 64^2x and we have to rewrite it with a base of 8 .
We know that 64 can be written in terms of 8 as the squared of 8 as:[tex] 64=8^2 [/tex].
Thus, the expression, [tex] 64^{2x} [/tex] can be rewritten as:
[tex] 64^{2x}=(8^2)^{2x} [/tex]
Now, using the rules of exponents we get:
[tex] (8^2)^{2x}=8^{2\times 2x}=8^{4x} [/tex]
[tex] \therefore 64^{2x}=8^{4x} [/tex]
Thus, out of the given options, option C is the correct option.
