Question

Tính:

\(\left(\frac{3}{7}\right)^{21}:\left(\frac{9}{49}\right)^6\)

Answer 1

(\(\frac{3}{7}\))²¹ : (\(\frac{9}{49}\))⁶       

  ^{=(\(\frac{3}{7}\))21 : [(\(\frac{3}{7}\))2]6}

   ^{= ( \(\frac{3}{7}\)})^{21 : (\(\frac{3}{7}\))12} 

   ^{= ( \(\frac{3}{7}\)})^{21-12  =} (\(\frac{3}{7}\))⁹ 

Answer 2

\(\left(\frac{3}{7}\right)^{21}:\left(\frac{9}{49}\right)^6=\left(\frac{3}{7}\right)^{21}:\left(\left(\frac{3}{7}\right)^2\right)^6=\left(\frac{3}{7}\right)^{21}:\left(\frac{3}{7}\right)^{2.6}=\left(\frac{3}{7}\right)^{21}:\left(\frac{3}{7}\right)^{12}\)

\(=\left(\frac{3}{7}\right)^{21-12}=\left(\frac{3}{7}\right)^9\)

Answer 3

\(\left(\frac{3}{7}\right)^{21}:\left(\frac{9}{49}\right)^6\\ =\left(\frac{3}{7}\right)^{21}:\left(\frac{3}{7}^2\right)^6\\ =\left(\frac{3}{7}\right)^{21}:\left(\frac{3}{7}\right)^{2.6}\\ =\left(\frac{3}{7}\right)^{21}:\left(\frac{3}{7}\right)^{12}\\ =\left(\frac{3}{7}\right)^{21-12}\\ =\left(\frac{3}{7}\right)^9\)

Answer 4

\(\left(\frac{3}{7}\right)^{21}:\left(\frac{9}{49}\right)^6=\frac{3}{7}.\left(\frac{3}{7}\right)^{20}:\left(\frac{9}{49}\right)^6=\frac{3}{7}.\left(\frac{3^2}{7^2}\right)^{10}:\left(\frac{9}{49}\right)^6\\ =\frac{3}{7}.\left(\frac{9}{49}\right)^{10}:\left(\frac{9}{49}\right)^6=\frac{3}{7}.\left(\frac{9}{49}\right)^4=\frac{3}{7}.\left(\frac{3^2}{7^2}\right)^6\)

\(\frac{3}{7}.\left(\frac{3}{7}\right)^{12}=\left(\frac{3}{7}\right)^{13}\)