Question
x^1/6•x^1/6
Using the properties of exponents which expression is equivalent
36 square root x
3 square root x
1/3 square root x
Square Root x
Using the properties of exponents which expression is equivalent
36 square root x
3 square root x
1/3 square root x
Square Root x
Answers
GPT-4o mini
To simplify the expression \( x^{1/6} \cdot x^{1/6} \) using the properties of exponents, you can apply the rule that states \( a^m \cdot a^n = a^{m+n} \).
In this case:
\[
x^{1/6} \cdot x^{1/6} = x^{1/6 + 1/6} = x^{2/6} = x^{1/3}
\]
Now, we can relate \( x^{1/3} \) to a square root.
Recall that:
\[
x^{1/3} = \sqrt[3]{x}
\]
However, the options provided show different expressions. Let's rewrite \( x^{1/3} \) in terms of the square root rather than a cube root.
We can also express \( \sqrt[3]{x} \) in relation to square roots. This is not directly among the options given.
To clarify, let’s compare the expression we derived \( x^{1/3} \) with the choices provided:
1. **36 square root x**: Equivalent to \( 36\sqrt{x} \) or \( 36x^{1/2} \)
2. **3 square root x**: Equivalent to \( 3\sqrt{x} \) or \( 3x^{1/2} \)
3. **1/3 square root x**: Equivalent to \( \frac{1}{3}\sqrt{x} \) or \( \frac{1}{3}x^{1/2} \)
4. **Square root x**: Equivalent to \( \sqrt{x} \) or \( x^{1/2} \)
Since none of the options involve \( x^{1/3} \), it seems there may be a misunderstanding in the choices. The simplified form \( x^{1/3} \) is not equal to any of the options provided.
Thus, the equivalent expression based on properties of exponents from \( x^{1/6} \cdot x^{1/6} \) is:
\[
x^{1/3}
\]
None of the provided choices are equivalent to \( x^{1/3} \). Please check the options again for any possible oversight.
In this case:
\[
x^{1/6} \cdot x^{1/6} = x^{1/6 + 1/6} = x^{2/6} = x^{1/3}
\]
Now, we can relate \( x^{1/3} \) to a square root.
Recall that:
\[
x^{1/3} = \sqrt[3]{x}
\]
However, the options provided show different expressions. Let's rewrite \( x^{1/3} \) in terms of the square root rather than a cube root.
We can also express \( \sqrt[3]{x} \) in relation to square roots. This is not directly among the options given.
To clarify, let’s compare the expression we derived \( x^{1/3} \) with the choices provided:
1. **36 square root x**: Equivalent to \( 36\sqrt{x} \) or \( 36x^{1/2} \)
2. **3 square root x**: Equivalent to \( 3\sqrt{x} \) or \( 3x^{1/2} \)
3. **1/3 square root x**: Equivalent to \( \frac{1}{3}\sqrt{x} \) or \( \frac{1}{3}x^{1/2} \)
4. **Square root x**: Equivalent to \( \sqrt{x} \) or \( x^{1/2} \)
Since none of the options involve \( x^{1/3} \), it seems there may be a misunderstanding in the choices. The simplified form \( x^{1/3} \) is not equal to any of the options provided.
Thus, the equivalent expression based on properties of exponents from \( x^{1/6} \cdot x^{1/6} \) is:
\[
x^{1/3}
\]
None of the provided choices are equivalent to \( x^{1/3} \). Please check the options again for any possible oversight.