# 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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d–There are typos (not p^1/6) and the solution is incorrect anyway. p^ (-2/3) ^ 2 is not -4/9. You add powers, you don’t multiply them.

Effortless Math Team–Thank you for your comment!

The answer is correct now. In fact, (-2/3) ^ 2 is 4/9.