Question

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

x−−√
Start Root x End Root

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

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

1x√3

Answer 1

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

So, we can calculate:

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

Now, let's find the equivalent expressions among the given options.

1. **\( \sqrt{x} \)** can be written as \( x^{1/2} \).
2. **\( \sqrt[36]{x} \)** can be written as \( x^{1/36} \).
3. **\( \sqrt[3]{x} \)** can be written as \( x^{1/3} \).
4. **\( \frac{1}{\sqrt[3]{x}} \)** can be written as \( x^{-1/3} \).

Since the expression \( x^{32} \) is not represented in any of the options given (as all options involve roots or negative exponents that are far less than 32), none of the responses provided is equivalent to \( x^{32} \).

Would you like to verify anything else regarding the properties of exponents?