Question

Using the properties of exponents and radicals, design at least three different equivalent forms of x². You must show how each one can be simplified back to x² in two or more steps. Stretch your mind and get creative! Keep in mind that something too simple, like x • x would not be acceptable since it takes only one step to convert it to x².

Answer 1

Ummm lemme give you an example, maybe it will give you some ideas how to solve this.

\[\Large \color{royalblue}{\left(x^2\right)^{3/2}} \quad=\quad x^{(2\cdot\frac{3}{2})} \quad=\quad x^{3}\]
That blue term represents another way of writing x^3.

Answer 2

When we have a term raised to a power and then a power again, rules of exponents tells us to `multiply` the exponents together.
So the 2 times 3/2 gives us 3.