Question

Using the properties of exponents, which expression is equivalent to x16⋅x16 ?(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
root index 3 Start Root x End Root

Answers

Answered by GPT-4o mini
To simplify the expression \( x^{16} \cdot x^{16} \) using the properties of exponents, we can apply the product of powers rule, which states that \( a^m \cdot a^n = a^{m+n} \).

In this case:

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

Now, we need to determine which of the given options is equivalent to \( x^{32} \). We can evaluate the options to see if any of them simplify to \( x^{32} \).

1. \( 1x\sqrt[3]{x} \) can be interpreted as \( x^{1/3} \), which is not \( x^{32} \).
2. \( \frac{1}{\sqrt[36]{x}} \) can be expressed as \( x^{-1/36} \), which is also not \( x^{32} \).
3. \( \sqrt{x} \) is the same as \( x^{1/2} \), not \( x^{32} \).
4. \( \sqrt[3]{x} \) is \( x^{1/3} \), and this is also not \( x^{32} \).

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

If there is any confusion about the interpretation of the options, I suggest checking the formulation, as \( x^{32} \) does not match any provided expressions.
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