Question

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

x−−√
Start Root x End Root

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

x−−√36
root index 36 Start Root x End Root

1x√3

Answer 1

Using the properties of exponents, which expression is equivalent to xx34 ?(1 point)
Responses

x4
x superscript 4 baseline

x
x

1​x√4
Start Fraction 1 over root index 4 Start Root x End Root End Fraction

x−−√4
root index 4 Start Root x End Root

Answer 2

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

Applying this property to the given expression:

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

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

Let's evaluate the options:

1. \( \sqrt{x} = x^{1/2} \) (not equivalent)
2. \( \sqrt[3]{x} = x^{1/3} \) (not equivalent)
3. \( \sqrt[36]{x} = x^{1/36} \) (not equivalent)
4. \( \frac{1}{\sqrt[3]{x}} = x^{-1/3} \) (not equivalent)

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

It appears there has been a misunderstanding in the options provided as none correspond to \( x^{32} \). If you have any additional context or specific instructions to follow, please let me know.

Answer 3

To simplify the expression \( x^{x^{34}} \), we need to recognize that this is already in a simplified form, presented as \( x^{34} \).

Since there might have been a typographical error or misunderstanding regarding the notation, let's interpret your question concerning finding an expression equivalent to \( x^{34} \).

**Given options:**
1. \( x^4 \) (not equivalent)
2. \( x \) (not equivalent)
3. \( \frac{1}{\sqrt[4]{x}} \) (which is \( x^{-1/4} \), not equivalent)
4. \( \sqrt[4]{x} \) (which is \( x^{1/4} \), not equivalent)

None of the provided options seem to match \( x^{34} \).

If we're looking for an expression equivalent to \( x^{34} \), we might conclude that none of the responses given are correct in terms of being equal to \( x^{34} \).

Please double-check the expression you provided and the available options. If you need further assistance, feel free to clarify!