Question

Find k and help with the equation!

Answer 1

Answer: k = 6+10x

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Work Shown:

`64*4^(5x)\\\\\left(2^6\right)*\left(2^(2)\right)^(5x)\\\\\left(2^6\right)*\left(2^(2*5x)\right)\\\\\left(2^6\right)*\left(2^(10x)\right)\\\\2^(6+10x)\\\\`

The result is in the form
`2^k` with k = 6+10x

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Step-by-step explanation:

First we need to get everything as an exponential expression with a base 2.

We rewrite 64 as
`2^6` and 4 as
`2^2` in the second step.

In the third step, I used the rule
`(a^b)^c = a^(b*c)` which says to multiply the exponents together. That's how I went from
`(2^2)^(5x)` to
`2^(2*5x)`. Then the 2*5x in the exponent becomes 10x.

To wrap things up, I used the rule
`a^b*a^c = a^(b+c)` which says to add the exponents when we multiply stuff of the same base together.