if you combine cube root of x and square root x what is the answer?

When combining the cube root of \( x \) and the square root of \( x \), you are multiplying the two expressions.

The cube root of \( x \) is written as \( x^{1/3} \), and the square root of \( x \) is written as \( x^{1/2} \). When you multiply these, you add the exponents according to the rules of exponents:

\[
x^{1/3} \times x^{1/2} = x^{\left(\frac{1}{3} + \frac{1}{2}\right)}.
\]

To add these fractions:

\[
\frac{1}{3} + \frac{1}{2} = \frac{2}{6} + \frac{3}{6} = \frac{5}{6}.
\]

So the result is:

\[
x^{5/6}.
\]

Thus, combining the cube root and square root of \( x \) gives \( x^{5/6} \).

Would you like further details or have any questions?

Here are 5 related questions:
1. How do you simplify expressions with higher roots?
2. What are the properties of exponents in fractional form?
3. How do you combine roots with different bases?
4. Can you solve for \( x \) if given \( x^{5/6} = 8 \)?
5. What happens if you divide roots instead of multiplying them?

**Tip**: When multiplying terms with the same base, remember to add the exponents!

Explore how to combine the cube root and square root of x using the laws of exponents. This guide breaks down the process step-by-step, showing how x^(1/3) and x^(1/2) combine to give x^(5/6). Ideal for students in Grades 9-11.

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