Question

Using the properties of exponents, which expression is equivalent to x1/6 • x1/6?

Answer 1

To simplify the expression \( x^{1/6} \cdot x^{1/6} \) using the properties of exponents, you can apply the product of powers rule, which states that when multiplying two expressions with the same base, you add their exponents.

Here’s how it works step-by-step:

1. Start with the expression:
\[
x^{1/6} \cdot x^{1/6}
\]

2. Apply the product of powers rule:
\[
x^{1/6 + 1/6}
\]

3. Add the exponents:
\[
1/6 + 1/6 = 2/6 = 1/3
\]

4. Therefore, the expression simplifies to:
\[
x^{1/3}
\]

Thus, the expression \( x^{1/6} \cdot x^{1/6} \) is equivalent to \( x^{1/3} \).