Question

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

x−−√
Start Root x End Root

1x√3
Start Fraction 1 over root index 3 Start Root x End Root End Fraction

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

x−−√36

Answer 1

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

So we have:
\[
x^{16} \cdot x^{16} = x^{16+16} = x^{32}
\]

Now we need to find which of the provided options is equivalent to \( x^{32} \).

1. **\( \sqrt{x} \)** can be expressed as \( x^{1/2} \).
2. **\( \frac{1}{\sqrt[3]{x}} \)** can be expressed as \( x^{-1/3} \).
3. **\( \sqrt[3]{x} \)** can be expressed as \( x^{1/3} \).
4. **\( \sqrt{36} \)** is just a number and does not involve \( x \).

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

Since it seems the options provided do not correspond to \( x^{32} \), please verify the options for possible re-examination or correction as none of them correspond with the exponentiation result \( x^{32} \).