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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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.