Question

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

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−−√
Start Root x End Root
x−−√3

Answer 1

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

So, we have:

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

Now, we need to see which of the given options is equivalent to \( x^{32} \).

1. \( \frac{1}{\sqrt[3]{x}} \) can be rewritten as \( x^{-1/3} \).
2. \( \sqrt[36]{x} \) is equal to \( x^{1/36} \).
3. \( \sqrt{x} \) is equal to \( x^{1/2} \).
4. \( \sqrt[3]{x} \) is equal to \( x^{1/3} \).

None of these options directly provide \( x^{32} \). If there is a mistake in interpreting the given options, please review them, as there is no expression listed that equals \( x^{32} \).

However, if we occasionally look for an answer that closely resembles or can be manipulated, we still find no direct correlation with \( x^{32} \) in the options provided.

If you meant to include \( x^{32} \) specifically in one of the options, please check all given options correctly. But as it stands, none of the options provided indicate equivalence to \( x^{32} \).