## Precalculus (6th Edition) Blitzer

$|x^3|$
RECALL: $\sqrt[n]{a^m} = a^{\frac{m}{n}}.$ Use the rule above to obtain $x^{\frac{12}{4}} \\=x^{3}.$ Note, however, that $x$ can be any real number. This means that when $x$ is negative, $x^3$ is also negative. Since the principal fourth root of an expression is nonegative, the answer above must be adjusted to $|x^3|.$ Thus, $\sqrt[4]{x^{12}} = |x^3|.$