Number Properties Puzzle – Challenge 19

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Number Properties Puzzle – Challenge 19


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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What people say about "Number Properties Puzzle – Challenge 19 - Effortless Math: We Help Students Learn to LOVE Mathematics"?

  1. 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.

    • Thank you for your comment!
      The answer is correct now. In fact, (-2/3) ^ 2 is 4/9.

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