Question

\(\dfrac{45^4.5^8}{75^6}\)

Answer 1

\(\dfrac{45^4.5^8}{75^6}=\dfrac{\left(5.9\right)^4.5^8}{\left(15.5\right)^6}=\dfrac{5^4.9^4.5^8}{15^6.5^6}=\dfrac{5^4.3^{2^4}.5^8}{\left(3.5\right)^6.5^6}=\dfrac{5^4.3^8.5^8}{3^6.5^6.5^6}=\dfrac{3^2.5^2}{5^2}=3^2=9\)

Answer 2

\(\dfrac{45^4.5^8}{75^6}=\dfrac{5^4.9^4.5^8}{3^6.5^6.5^6}=\dfrac{1.\left(3^2\right)^4.5^2}{3^6.5^2.1}=\dfrac{3^8.1}{3^6.1}=\dfrac{3^8}{3^6}=\dfrac{3^2}{1}=9\)