Question

Using the properties of exponents, which expression is equivalent to x16⋅x16 ?(1 point)
Responses

x−−√
Start Root x End Root

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

Answer 1

To simplify the expression \( x^{16} \cdot x^{16} \), we can use the property of exponents that states \( a^m \cdot a^n = a^{m+n} \).

Applying this property:

\[
x^{16} \cdot x^{16} = x^{16+16} = x^{32}
\]

Now, we need to compare this with the given options:

1. \( \sqrt{x} \)
2. \( \sqrt[3]{x} \)
3. \( \frac{1}{\sqrt[3]{x}} \)
4. \( \sqrt{36} \)

None of these options directly represent \( x^{32} \) because they involve roots rather than exponentiation. Thus, none of the provided choices are equivalent to \( x^{32} \).

If your intention was to find an expression of the form \( x^n \) rather than one of the given answers, \( x^{32} \) is the correct equivalent form. However, if there's something specific you want to find among the options, please clarify!