Using the properties of exponents, which expression is equivalent to x1/6⋅x1/6? (1 point)

Question

Responses

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

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

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

x−−√

Answer 1

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

So, we have:

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

The expression \( x^{1/3} \) is equivalent to \( \sqrt[3]{x} \) (the cube root of \( x \)).

Now, looking at the provided responses:

• \( x^{- \sqrt{3}} \)
• \( \frac{1}{\sqrt[3]{x}} \)
• \( x^{- \sqrt{36}} \)
• \( \sqrt[3]{x} \)

The equivalent expression to \( x^{1/3} \) from the options given is \( \sqrt[3]{x} \).

Thus, the correct response is:

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