Question

Answer 1

a) \(\dfrac{3^2.27^4}{9^3}=\dfrac{3^2.\left(3^3\right)^4}{\left(3^2\right)^3}=\dfrac{3^2.3^{12}}{3^6}=3^{2+12-6}=3^8\)

b) \(\dfrac{3^4.3^5}{3^3}=3^{4+5-3}=3^6\)

c) \(\dfrac{2^3.8^3}{4^5}=\dfrac{2^3.\left(2^3\right)^3}{\left(2^2\right)^5}=\dfrac{2^3.2^9}{2^{10}}=2^{3+9-10}=2^2\)

d) \(\dfrac{125^2:25^2}{5^4}=\dfrac{\left(5^3\right)^2:\left(5^2\right)^2}{5^4}=\dfrac{5^6:5^2}{5^4}=5^{6-2-4}=5^0=1\)