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

Question

Responses

x−−√3
root index 3 Start Root x End Root

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−−√

Answer 1

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

So, in this case:

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

Now, let’s look through the options provided and see if any of them can be simplified to \( x^{32} \):

1. \(\sqrt[3]{x}\) can be written as \( x^{1/3} \)
2. \(\sqrt[36]{x}\) can be written as \( x^{1/36} \)
3. \(\frac{1}{\sqrt[3]{x}} = \frac{1}{x^{1/3}} = x^{-1/3} \)
4. \(\sqrt{x}\) can be written as \( x^{1/2} \)

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

It appears that none of the proposed options is the answer to the given expression \( x^{16} \cdot x^{16} \).

If you intended to provide options that could be simplified to \( x^{32} \) or if there was an error in the options, please double-check. If you have more options or clarifications, feel free to share!