Question

2^12 .3^5 -4^6.81 / 12^5 +2^7 .18^3

Answer 1

\(\dfrac{2^{12}.3^5-4^6.81}{12^5+2^7.18^3}\)

\(=\dfrac{2^{12}.3^5-\left(2^2\right)^6.3^4}{\left(2^2.3\right)^5+2^7.\left(2.3^2\right)^3}\)

\(=\dfrac{2^{12}.3^5-2^{12}.3^4}{2^{10}.3^5+2^7.2^3.3^6}\)

\(=\dfrac{2^{12}.3^4.\left(3-1\right)}{2^{10}.3^5+2^{10}.3^6}\)

\(=\dfrac{2^{12}.3^4.2}{2^{10}.3^5.\left(1+3\right)}\)

\(=\dfrac{2^2.2}{3.4}=\dfrac{2}{3}\)

#$\mathtt{Toru}$

Answer 2

=\(\dfrac{2^{12}.3^5-\left(2^2\right)^6.3^4}{\left(2^2.3\right)^5+2^7.\left(2.3^2\right)^3}\)

=\(\dfrac{2^{12}.3^5-2^{12}.3^4}{2^{10}.3^5+2^7.2^3.3^6}\)

=\(\dfrac{2^{12}.3^4.\left(3-1\right)}{2^{10}.3^5+2^{10}.3^6}\)

=\(\dfrac{2^{12}.2.3^4}{2^{10}.3^5.\left(3+1\right)}\)

=\(\dfrac{2^{13}.3^4}{2^{12}.3^5}\)

=\(\dfrac{2}{3}\)