Number Properties Puzzle – Challenge 19

Challenge:

If (t^{frac{1}{2}} = p^{frac{-2}{3}}) and (p^{frac{1}{2}} = z^{frac{-3}{5}}), what is the value of t in terms of z?

The Absolute Best Book to Challenge Your Smart Student!

To find t in terms of z, first we need to find the value of t in terms of p:
(t^{frac{1}{2}} = p^{frac{-2}{3}} → (t^{frac{1}{2}})^2= (p^{frac{-2}{3}})^2 → t = p^{frac{4}{9}})
Now, solve for p
(p^{frac{1}{2}} = z^{frac{-3}{5}} →(p^{frac{1}{2}} )^2 = (z^{frac{-3}{5}})^2 → p =z^{frac{9}{25}}→)
(p^{frac{4}{9}} = z^{frac{4}{25}} →)
(t = p^{frac{4}{9}}) and ((p)^{frac{4}{9}} = z^{frac{4}{25}}), therefore, (t =z^{frac{4}{25}})

The Absolute Best Books to Ace Algebra