# 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?

### The Absolute Best Book to challenge your Smart Student!

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, $$t =z^{\frac{4}{25}}$$ #### Effortless Math Educations

1. d says:

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 says:

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

36% OFF

X

## How Does It Work? ### 1. Find eBooks

Locate the eBook you wish to purchase by searching for the test or title.  ### 3. Checkout

Complete the quick and easy checkout process. ## Why Buy eBook From Effortlessmath? Save up to 70% compared to print  Help save the environment  Over 2,000 Test Prep titles available Over 80,000 happy customers Over 10,000 reviews with an average rating of 4.5 out of 5  