Question

a,72^3 . 54^2 / 108^4 

b, 3^10 . 11 + 3^10 .5 / 3^9 . 2^4

Answer 1

a) \(\frac{72^3.54^2}{108^4}\)

\(=\frac{\left(2^3.3^2\right)^3.\left(2.3^2\right)^2}{\left(2^2.3^2\right)^4}\)

\(=\frac{2^9.3^6.2^2.6^6}{2^8.3^{12}}=2^3\)

\(=8\)

b) \(\frac{3^{10}.11+3^{10}.5}{3^9.2^4}\)

\(=\frac{3^{10}.\left(11+5\right)}{3^9.2^4}\)

\(=\frac{3^{10}.2^4}{3^9.2^4}\)

\(=3\)