Question

(y = 2^{-x}). Write this in an equivalent way with a tional base.

a) (y = {1}{2^x})
b) (y = {1}{2}^{-x})
c) (y = {2}{x})
d) (y = {1}{2^x})

Answer 1

To write the equation y = 2^{-x} in an equivalent way with a rational base, take the reciprocal of the base, 2, and raise it to the power of the absolute value of the original exponent. This yields y = 1/2^x.

Step-by-step explanation:

To write the equation y = 2^{-x} in an equivalent way with a rational base, we need to express the exponent -x as a positive exponent. To do this, we can take the reciprocal of the base, which is 2, and raise it to the power of the absolute value of the original exponent. This gives us:

y = 2^{-x} = \frac{1}{2^x}

So the correct answer is (a) (y = \frac{1}{2^x}).