Question

If 1/64=4^2s-1 times 16^2s+2 what is the value of s?

Answer 1

s=-1 see attachment for explanation

Answer 2

Answer: s=-1

Explanation:

We can re-write the equation as follows:

$\frac{1}{64}=(4^{2s-1})(16^{2s+2})$

Let's rewrite the terms on the left and on the right as follows:

$2^{-6} = ((2^2)^{2s-1})((2^4)^{2s+2})$

So we have

$2^{-6} = (2^{2(2s-1)})(2^{4(2s+2)})$

Now we can use the following rule:

$x^{a+b}=x^a x^b$

to rewrite the term on the right:

$(2^{2(2s-1)})(2^{4(2s+2)})=2^{2(2s-1)+4(2s+2)}$

So now we have

$2^{-6}=2^{2(2s-1)+4(2s+2)}$

and since the bases are the same, we can just equalize the exponents:

$-6=2(2s-1)+4(2s+2)$

$-6=4s-2+8s+8\\-12 = 12 s\\s=-1$