Answer:
[tex]4x[/tex]
Step-by-step explanation:
We want to find the simplest rational exponent form of
[tex]\sqrt{x} \cdot 4\sqrt{x}[/tex]
Recall that: [tex]\sqrt{a}=a^{\frac{1}{2} }[/tex]
We rewrite the expression in the exponent form to get:
[tex]x^{\frac{1}{2}}\cdot 4x^{\frac{1}{2}[/tex]
We can regroup the product to get:
[tex]4 x^{\frac{1}{2}\cdot x^{\frac{1}{2}[/tex]
We apply the rule: [tex]a^m\cdot a^n=a6{m+n}[/tex] to get:
[tex]4 x^{\frac{1}{2}}\cdot x^{\frac{1}{2}=4 x^{\frac{1}{2}+\frac{1}{2}}[/tex]
[tex]4 x^{\frac{1}{2}}\cdot x^{\frac{1}{2}=4 x^{1}[/tex]
[tex]4 x^{\frac{1}{2}}\cdot x^{\frac{1}{2}=4x[/tex]
