Question

Using the properties of exponents, which expression is equivalent to x16⋅x16
?(1 point)
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−−√
Start Root x End Root

x−−√36

Answer 1

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

Applying this rule:

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

Now, let's look at the given options to find an equivalent expression to \(x^{32}\):

1. \( \sqrt[3]{x} \) is equivalent to \( x^{1/3} \).
2. \( \frac{1}{\sqrt[3]{x}} \) is equivalent to \( x^{-1/3} \).
3. \( \sqrt{x} \) is equivalent to \( x^{1/2} \).
4. \( \sqrt{36} \) is a constant and does not involve \( x \).

None of these options are equivalent to \( x^{32} \).

Therefore, no option provided represents the equivalent expression to \( x^{16} \cdot x^{16} \). If you have more options or a different context to provide, I can help further!