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\frac{\left(12\sqrt{2}\right)^{2}}{17^{2}}
To raise \frac{12\sqrt{2}}{17} to a power, raise both numerator and denominator to the power and then divide.
\frac{12^{2}\left(\sqrt{2}\right)^{2}}{17^{2}}
Expand \left(12\sqrt{2}\right)^{2}.
\frac{144\left(\sqrt{2}\right)^{2}}{17^{2}}
Calculate 12 to the power of 2 and get 144.
\frac{144\times 2}{17^{2}}
The square of \sqrt{2} is 2.
\frac{288}{17^{2}}
Multiply 144 and 2 to get 288.
\frac{288}{289}
Calculate 17 to the power of 2 and get 289.