# Number Properties Puzzle – Challenge 19

Enjoy working with numbers and solving puzzles? Test your mind with this tough math challenge. Let's challenge your brain!

## 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?

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The correct answer is $$z^{\frac{4}{25}}$$.

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, $$t =z^{\frac{4}{25}}$$

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