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

sqrt(x^4) ?

Answer 2

I don't understand what it's asking me to do. Like I need 3 different equations that can be simplified down to x^2 but in 2+ steps

Answer 3

It's like building a exponential equation exercise, in other words, let's begin with x^2 :
\[x ^{2}\]
Nice... Now, I think I'll add some division (wich implied the sustraction of exponents)
\[\frac{ x ^{4} }{ x ^{2} }\]
Looks fun... I'll add some radicals.
\[\frac{ \sqrt[]{x ^{8}} }{ \sqrt{x ^{4}} }\]
I'll create another one, a multiplication that makes everything 1.
meaning i'm searching for a exponent equal to zero:
\[(\frac{ \sqrt{x^{8}} }{ \sqrt{x ^{4}} })(\frac{ y ^{3} }{ y ^{3} })\]
To make thing more fun, I'll transform each of y^3 in radicals and get rid of the parenthesis:
\[\frac{ \sqrt[3]{y ^{6}}\sqrt{x ^{8}} }{ \sqrt[4]{y ^{12}}\sqrt{x ^{4}} }\]
And that's just an example, just play around with the properties.

Answer 4

Thank you so much