Question

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

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 \( x^{16} \cdot x^{16} \), 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, let's analyze the given responses to find an equivalent expression to \( x^{32} \):

1. **Start Root x End Root** is equivalent to \( x^{1/2} \).

2. **root index 36 Start Root x End Root** is equivalent to \( x^{1/36} \).

3. **root index 3 Start Root x End Root** is equivalent to \( x^{1/3} \).

4. **1x√3** is equivalent to \( \frac{1}{x \sqrt{3}} \).

None of these expressions directly represent \( x^{32} \). However, if we're looking for an expression that is equivalent to \( x^{32} \) based on the options provided, we can conclude that none of the given options represent \( x^{32} \) directly.

If the question is strictly about identifying the equivalent of \( x^{32} \), the answer is that none of these options fit. However, if you were looking for a representation that might have been simplified incorrectly, double-checking the options or the context might be necessary.