Question

Rewrite g (x) = 3^-x when x = 7/5. Write this as an expression with a positive rational exponent and as an expression involving a radical. Show where g (7/5) would be located on the graph.

Answer 1

Explanation:

g(x) = 3^-x

x = 7/5

so,

3^-(7/5)

the "-" says "1/...", therefore

1/(3^(7/5))

that is the expressing with the positive rational exponent.

with a fractional a/b exponent, "a" means "to the power of", and "b" means "pull the bth root".

so,

1/(3^(7/5)) =

`\frac{1}{ \sqrt[5]{ {3}^(7) } }`

that is the expression with a radical.

to find the point find the origin (0, 0) point. from there go eighth on the x-axis to 7/5 = 1.4. and from there you go straight up to the curve. that is the point of g(7/5).

1/(3^(7/5)) = 0.214798005...

that is what the y value would be of that point.

by the way, the graph in the picture does not match the actual graph.