Question

simplify. assume all variables are positive.
$(cd)^{\frac{1}{4}}$
write your answer in the form $a$ or $\frac{a}{b}$, where $a$ and $b$ are constants or variable expressions that have no variables in common. all exponents in your answer should be positive.

Explanation:

Step1: Apply the power of a product rule

The power of a product rule states that \((ab)^n = a^n b^n\). For \((cd)^{\frac{1}{4}}\), we apply this rule:
$$(cd)^{\frac{1}{4}} = c^{\frac{1}{4}} d^{\frac{1}{4}}$$
We can also write this using radical notation as \(\sqrt[4]{c}\sqrt[4]{d}\) or combined as \(\sqrt[4]{cd}\), but in exponential form with positive exponents (and since \(c\) and \(d\) have no variables in common), \(c^{\frac{1}{4}} d^{\frac{1}{4}}\) (or \(\sqrt[4]{cd}\)) is in the correct form.

Answer:

\(c^{\frac{1}{4}}d^{\frac{1}{4}}\) (or \(\sqrt[4]{cd}\))