Question

Rewrite in simplest rational exponent form √x • 4√x. Show each step of your process.

Answer 1

$First\ step:you\ must\ have\ the\ domain\ (D)\\x\geq0\to D:x\in[0;\ \infty)\\\\Second\ step:use\ \sqrt{a}\cdot\sqrt{a}=\left(\sqrt{a}\right)^2=a\ for\ a\geq0\\\\Solution:\\\sqrt{x}\cdot4\sqrt{x}=4(\sqrt{x})^2=\huge\boxed{4x}$

$or\ other\ method\\\\First\ step:\ use\ \sqrt{x}=x^{\frac{1}{2}}\\\\\sqrt{x}\cdot4\sqrt{x}=x^\frac{1}{2}\cdot4x^{\frac{1}{2}}\\\\Second\ step:\ use\ a^n\cdot a^m=a^{n+m}\\\\x^\frac{1}{2}\cdot4x^{\frac{1}{2}}=4\cdot x^\frac{1}{2}\cdot x^{\frac{1}{2}}=4x^{\frac{1}{2}+\frac{1}{2}}=4x^1=\huge\boxed{4x}$