To calculate \((\frac{7}{4})^{11}\), we can first calculate \(7^{11}\) and \(4^{11}\) separately, and then we'll divide the two results. 1. Calculate \(7^{11}\): \[ 7^{11} = 19487171 \] 2. Calculate \(4^{11}\): \[ 4^{11} = (2^2)^{11} = 2^{22} = 4194304 \] 3. Now divide the two results: \[ \frac{7^{11}}{4^{11}} = \frac{19487171}{4194304} \approx 4.638 \] Thus, \((\frac{7}{4})^{11} \approx 4.638\). To summarize: \[ \left(\frac{7}{4}\right)^{11} \approx 4.638 \]

(7/4)^11

1 answer

To calculate \((\frac{7}{4})^{11}\), we can first calculate \(7^{11}\) and \(4^{11}\) separately, and then we'll divide the two results.

Calculate \(7^{11}\): \[ 7^{11} = 19487171 \]
Calculate \(4^{11}\): \[ 4^{11} = (2^2)^{11} = 2^{22} = 4194304 \]
Now divide the two results: \[ \frac{7^{11}}{4^{11}} = \frac{19487171}{4194304} \approx 4.638 \]

Thus, \((\frac{7}{4})^{11} \approx 4.638\).

To summarize: \[ \left(\frac{7}{4}\right)^{11} \approx 4.638 \]