Number Properties Puzzle – Challenge 19
Number Properties Puzzle - Challenge 19 is a multiple-choice math challenge from Effortless Math. Read the problem, choose from the answer options below, then open the solution to see the full step-by-step working and check your reasoning against it.
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}})The Absolute Best Books to Ace Algebra
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