Question

given x = 2^p and y = 2^q, express in terms of x and/or y

I) 2^p+q

II) 2^2p

III) 2^q-1

Answer 1

Answer:

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2^ (p + q) = 2^p • 2^q because you'd add the exponents, so xy

2^ 2q = 2^(q + q) = 2^q • 2^q as above, so y^2

2^ (p-1) = 2^p / 2^1 because you subtract exponents when dividing, so x/2

If xy = 32 then x = 32/y

so 2xy^2 would = 2(32/y)•y^2 = 64y = 32 so y = 1/2

making x = 64 since xy = 32

so 64 = 2^p; p = 6

1/2 = 2^q; q = -1