Question

[( 3^14 x 69 + 3^14 x 12 ) : 3^16 -7] : 2^4

Answer 1

\(\left[\left(3^{14}\times69+3^{14}\times12\right):3^{16}-7\right]:2^4\)

\(=\left[3^{14}\left(69+12\right):3^{16}-7\right]:2^4\)

\(=\left[3^{14}.81:3^{16}-7\right]:2^4\)

\(=\left[3^{14}.3^4:3^{16}-7\right]:2^4\)

\(=\left[3^2-7\right]:2^4\)

\(=2:2^4\)

\(=\dfrac{2}{16}=\dfrac{1}{8}\)

Answer 2

\(\left[\left(3^{14}.69+3^{14}.12\right):3^{16}-7\right]:2^4\\ =\left[3^{14}.\left(69+12\right):3^{16}-7\right]:2^4\\ =\left[3^{14}.81:3^{16}-7\right]:2^4\\ =\left[3^{14}.3^4:3^{16}-7\right]:2^4\\ =\left(3^2-7\right):2^4=2:2^4=\dfrac{1}{2^3}=\dfrac{1}{8}\)

Answer 3

\(=\left(\dfrac{3^{14}\cdot\left(69+12\right)}{3^{16}}-7\right):2^4\)

=(3^2-7):2^4

=2:2^4=1/8