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

@Akeller27 and @callie2240

Answer 2

One form is the square root of x to the fourth power:
(x^4)^1/2

Another form is the fourth root of x to the eighth power:
(x^8)^1/4

Another form is the eighth root of x to the sixteenth power:
(x^16)^1/8

Each one can be simplified to x^2 by multiplying the exponent within the parenthesis with the external exponent.

Answer 3

Alright I need to come up with some that need more then 1 step

Answer 4

thanks for the examples though

Answer 5

hmm how would I add another step onto it lol?

Answer 6

Since you need radicals...

\[(x ^{\frac{ 3 }{ 2 }}) (\frac{ 1 }{ \sqrt{x}}) (\sqrt{x}) (\sqrt{x})\]

Answer 7

lost connection