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

Answer 1

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

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

Now, we need to find an equivalent expression to \( x^{32} \) among the given options.

1. \( 1 x \sqrt{3} \) (does not match)
2. \( \frac{1}{\sqrt[3]{x}} \) (does not match)
3. \( \sqrt[36]{x} \) (this is \( x^{1/36} \), does not match)
4. \( \sqrt{x} \) (this is \( x^{1/2} \), does not match)
5. \( \sqrt[3]{x} \) (this is \( x^{1/3} \), does not match)

None of the options provided directly correspond to \( x^{32} \).

There might be a miscommunication about the options provided or missing option corresponding to \( x^{32} \). Please check if there is an option indicating \( x^{32} \) or any similar expression based on exponent properties you would like evaluated.