Question

Rewrite the expression with the given base.

64^2x with a base of 8

A. (4^3)^2x

B. 2(8^2x)

C. 8^4x

D. 8^2x+2

Answer 1

C. 8^4x
64^2x = 4096x
8^4x= 4096x

Answer 2

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:
`64=8^2`.

Thus, the expression,
`64^(2x)` can be rewritten as:

`64^(2x)=(8^2)^(2x)`

Now, using the rules of exponents we get:

`(8^2)^(2x)=8^(2* 2x)=8^(4x)`

`\therefore 64^(2x)=8^(4x)`

Thus, out of the given options, option C is the correct option.