Express in simplest radical form.
x, cubed, square root of, x, to the power 7 , end square root
x 
3
  
x 
7
 
​	
 


To simplify the expression:

\[
x \cdot \sqrt[3]{x^7}
\]

### Step 1: Simplify the cube root part.
\[
\sqrt[3]{x^7} = x^{7/3}
\]

### Step 2: Combine the \(x\) terms.
The original expression is \(x \cdot x^{7/3}\). You can add the exponents (since the bases are the same):

\[
x^1 \cdot x^{7/3} = x^{1 + 7/3}
\]

Convert 1 into a fraction:

\[
1 = \frac{3}{3}
\]

Now, add the exponents:

\[
x^{\frac{3}{3} + \frac{7}{3}} = x^{\frac{10}{3}}
\]

So, the expression in simplest radical form is:

\[
x^{\frac{10}{3}}
\]

Would you like further clarification or details?

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### Related Questions:
1. How do you simplify expressions with fractional exponents?
2. What are the rules for adding exponents with different bases?
3. How do you convert between radical notation and fractional exponents?
4. What is the general process for simplifying cube roots?
5. How does the product of powers rule work with different types of exponents?

**Tip:** When simplifying expressions with radicals and exponents, always try to rewrite radicals as fractional exponents first for easier manipulation!

Express in simplest radical form. x cubed, square root of, x to the power 7.

Learn how to simplify the expression x ⋅ ∛x⁷. This solution involves key algebraic concepts such as cube roots, exponents, and their simplification. Ideal for students in Grades 9-11, this step-by-step guide covers exponent rules and radical conversions.

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