Using the properties of exponents, which expression is equivalent to x^1/6⋅x^1/6 ?(1 point)

To solve this problem, we will use the properties of exponents. Specifically, when multiplying expressions with the same base, we add their exponents:

\[
x^{\frac{1}{6}} \cdot x^{\frac{1}{6}} = x^{\left(\frac{1}{6} + \frac{1}{6}\right)}.
\]

Now, let's add the exponents:

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

So, the expression simplifies to:

\[
x^{\frac{1}{3}}.
\]

**Therefore, the equivalent expression is \(x^{\frac{1}{3}}\).**

Would you like further explanation or have any questions?

Here are some related questions you might find useful:
1. How do you multiply powers with the same base?
2. What is the result of \( x^{1/4} \cdot x^{1/4} \)?
3. How do you simplify \( x^{a} \cdot x^{b} \)?
4. How can you convert fractional exponents to radicals?
5. What is the equivalent expression of \( x^{1/2} \cdot x^{1/2} \)?

**Tip:** When multiplying powers with the same base, always add the exponents!

Using the properties of exponents, which expression is equivalent to x^1/6⋅x^1/6?

Understand how to simplify x^1/6 ⋅ x^1/6 using the properties of exponents. This step-by-step guide demonstrates how to add exponents when multiplying powers with the same base, resulting in x^1/3. Ideal for students in Grades 8-10.

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