Using the properties of exponents which expression is equivalent to x^1/6* x^1/6

Answer 1

To simplify the expression \( x^{1/6} \cdot x^{1/6} \), we can use the property of exponents that states:

\[ a^m \cdot a^n = a^{m+n} \]

In this case, \( m \) and \( n \) are both \( \frac{1}{6} \):

\[ x^{1/6} \cdot x^{1/6} = x^{1/6 + 1/6} = x^{2/6} \]

Now, simplify \( \frac{2}{6} \):

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

Thus, the expression simplifies to:

\[ x^{1/3} \]

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