Using the properties of exponents, which expression is equivalent to x 1/6 times x 1/6

Question

?(1 point)
Responses

x−−√36
root index 36 Start Root x End Root

1x√3
Start Fraction 1 over root index 3 Start Root x End Root End Fraction

x−−√3
root index 3 Start Root x End Root

x−−√
Start Root x End Root

Answer 1

To simplify the expression \( x^{1/6} \times x^{1/6} \), we can use the properties of exponents. According to the property that states \( a^m \times a^n = a^{m+n} \), we can add the exponents together.

So,

\[ x^{1/6} \times x^{1/6} = x^{(1/6) + (1/6)} = x^{2/6} = x^{1/3} \]

Now, \( x^{1/3} \) can also be expressed in radical form as \( \sqrt[3]{x} \).

Among the given options, the correct equivalent expression for \( x^{1/6} \times x^{1/6} \) is:

\( \sqrt[3]{x} \)

Thus, the equivalent expression is:

\( x^{-\sqrt[3]{x}} \) which seems like a typo or confusion in your options, ensuring we really meant to clarify it should just be noted as \( \sqrt[3]{x} \).