Question: Simplify. \(\sqrt{u^{19}}\) Assume that the variable represents a positive real number…

Simplify.

\(\sqrt{u^{19}}\)

Assume that the variable represents a positive real number.

\(\sqrt{\square}\)

Solution

To simplify the expression \(\sqrt{u^{19}}\), we can use the property of exponents that says \(\sqrt{x} = x^{1/2}\). First, we rewrite the expression using this property: \[ \sqrt{u^{19}} = (u^{19})^{1/2} \] Next, we apply the power of a power property \((a^m)^n = a^{m \cdot n}\): \[ (u^{19})^{1/2} = u^{19 \cdot \frac{1}{2}} = u^{19/2} \] Thus, the simplified expression is: \[ u^{19/2} \]