Using the properties of exponents, which expression is equivalent to x16⋅x16

Question

?(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
only answer with the options i gave you

Answer 1

The expression \( x^{16} \cdot x^{16} \) can be simplified using the properties of exponents. Specifically, when multiplying two expressions with the same base, you can add the exponents:

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

Now, we need to express \( x^{32} \) using the options provided.

From the options given:

1. \( \frac{1}{\sqrt[3]{\sqrt{x}}} \)
2. \( \sqrt[36]{x} \)
3. \( \sqrt{x} \)
4. \( \sqrt[3]{x} \)

None of the responses seem to directly represent \( x^{32} \).

Instead, let's assess the expression:

\[ \sqrt{x} = x^{1/2}, \quad \sqrt[3]{x} = x^{1/3}, \quad \sqrt[36]{x} = x^{1/36} \]

Since none of these options equal to \( x^{32} \), it appears there might have been an issue with the listed choices.

However, strictly based on the format of the existing responses, \( x^{32} \) would not match any presented options and thus, none should be selected as equivalent.

Please provide further clarification or additional options if needed.