Question

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

x−−√
square root of x

1x√3
the fraction with numerator 1 and denominator cube root of x

x−−√3
cube root of x

x−−√36

Answer 1

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

So,

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

Now, let's analyze the given responses to see which one is equivalent to \( x^{32} \):

1. \( \sqrt{x} = x^{1/2} \)
2. \( \frac{1}{\sqrt[3]{x}} = x^{-1/3} \)
3. \( \sqrt[3]{x} = x^{1/3} \)
4. \( \sqrt[6]{x} = x^{1/6} \) (but this option seems to be written incorrectly as \( x^{-\sqrt{36}} \), which should be interpreted as \( x^{-\sqrt{6}} \))

None of the choices simplify to \( x^{32} \).

Thus, none of the provided responses are equivalent to \( x^{32} \).

If you were looking for a correct equivalent expression, it would simply be \( x^{32} \).