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

Question

Responses

x−−√36
root index 36 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−−√3

Answer 1

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

Here, we have:

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

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

1. \( \sqrt[36]{x} \) means \( x^{1/36} \) (not equivalent).
2. \( \frac{1}{\sqrt[3]{x}} \) means \( x^{-1/3} \) (not equivalent).
3. \( \sqrt{x} \) means \( x^{1/2} \) (not equivalent).
4. \( \sqrt[3]{x} \) means \( x^{1/3} \) (not equivalent).

None of the provided responses match \( x^{32} \).

It appears there may not be an equivalent expression among those provided since all options do not equal \( x^{32} \). If you meant to list an expression that matches \( x^{32} \) directly, please provide it, and I can help confirm if it's correct. Otherwise, from the available options, none are equivalent to \( x^{32} \).