The expression in the image is:

$(\sqrt{x})(x^2 + 2)$

Step-by-step solution:

We will simplify this by distributing $\sqrt{x}$ to both terms inside the parentheses:

$\sqrt{x} \cdot (x^2 + 2) = \sqrt{x} \cdot x^2 + \sqrt{x} \cdot 2$

1. First term: $\sqrt{x} \cdot x^2 = x^{\frac{1}{2}} \cdot x^2 = x^{\frac{5}{2}}$ (using the property of exponents: $a^m \cdot a^n = a^{m+n}$).
2. Second term: $\sqrt{x} \cdot 2 = 2\sqrt{x}$.

Final result:

$x^{\frac{5}{2}} + 2\sqrt{x}$

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Would you like me to expand further, such as explaining how to handle these terms in specific applications or graphing?

Related Questions:

1. What is the domain of this expression?
2. How can this expression be used in solving equations?
3. How would this expression be represented visually on a graph?
4. What are the rules of exponents and radicals used in simplifying this?
5. How can you factor expressions involving square roots?

Tip:

Always remember that $\sqrt{x} = x^{\frac{1}{2}}$ helps in combining terms with similar bases using exponent rules!