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Let’s check out your problem:

sqrt((3^(a))/(7^(6)))=(9sqrt7)/(7^(2))

3a76=9772 \sqrt{\frac{3^{a}}{7^{6}}}=\frac{9 \sqrt{7}}{7^{2}}

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Full solution

Q. 3a76=9772 \sqrt{\frac{3^{a}}{7^{6}}}=\frac{9 \sqrt{7}}{7^{2}}
  1. Square both sides: Square both sides to get rid of the square root. (3a76)=(9772)2\left(\frac{3^{a}}{7^{6}}\right) = \left(\frac{9\sqrt{7}}{7^{2}}\right)^{2}
  2. Calculate square: Calculate the square of the right side. (3a76)=92×774\left(\frac{3^{a}}{7^{6}}\right) = \frac{9^{2} \times 7}{7^{4}}
  3. Simplify right side: Simplify the right side.\newline(3a76)=81×774\left(\frac{3^{a}}{7^{6}}\right) = \frac{81 \times 7}{7^{4}}
  4. Reduce fraction: Reduce the fraction by canceling out common factors.\newline(3a76)=8173(\frac{3^{a}}{7^{6}}) = \frac{81}{7^3}
  5. Express 8181: Express 8181 as 33 to the power of 44.(3a76)=3473\left(\frac{3^{a}}{7^{6}}\right) = \frac{3^{4}}{7^{3}}
  6. Set exponents equal: Since the bases are now the same, set the exponents equal to each other. a=4a = 4

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