Question
match the expressions that are equivalent to the ones outlined below (7/2)^-4
Answers
GPT-4o mini
To find an equivalent expression for \((\frac{7}{2})^{-4}\), we can utilize the properties of exponents. The negative exponent indicates that we should take the reciprocal of the base raised to the positive exponent.
1. Start with the original expression:
\[
\left(\frac{7}{2}\right)^{-4}
\]
2. Apply the negative exponent property:
\[
\left(\frac{7}{2}\right)^{-4} = \frac{1}{\left(\frac{7}{2}\right)^4}
\]
3. Compute the expression with a positive exponent:
\[
\left(\frac{7}{2}\right)^4 = \frac{7^4}{2^4} = \frac{2401}{16}
\]
4. Therefore, the expression simplifies to:
\[
\left(\frac{7}{2}\right)^{-4} = \frac{1}{\frac{2401}{16}} = \frac{16}{2401}
\]
So the equivalent expression for \((\frac{7}{2})^{-4}\) is \(\frac{16}{2401}\).
If you have more expressions that you would like to match with this one, please list them for me!
1. Start with the original expression:
\[
\left(\frac{7}{2}\right)^{-4}
\]
2. Apply the negative exponent property:
\[
\left(\frac{7}{2}\right)^{-4} = \frac{1}{\left(\frac{7}{2}\right)^4}
\]
3. Compute the expression with a positive exponent:
\[
\left(\frac{7}{2}\right)^4 = \frac{7^4}{2^4} = \frac{2401}{16}
\]
4. Therefore, the expression simplifies to:
\[
\left(\frac{7}{2}\right)^{-4} = \frac{1}{\frac{2401}{16}} = \frac{16}{2401}
\]
So the equivalent expression for \((\frac{7}{2})^{-4}\) is \(\frac{16}{2401}\).
If you have more expressions that you would like to match with this one, please list them for me!