Question

HELP ??

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

use this property
\[\large \sqrt{x^{n}} = x^{n/2}\]
and
\[\large \sqrt[m]{x^{n}} = x^{n/m}\]
so
\[\large \sqrt{x^{2}}*\sqrt{x^{2}} = x^{2}\]
\[\large \sqrt[4]{x^{4}}*\sqrt[4]{x^{4}} = x^{2}\]

Answer 2

\[(\sqrt[3]{x^2})^(4/3)\]

\[\sqrt{\sqrt{\sqrt{x^16}}}\]

\[(-3x-4+4x+4)^2\]

Answer 3

You both put something different ... D: