Question

Answer 1

1: \(\dfrac{\left(1+2+3+4\right)^2}{1^3+2^3+3^3+4^3}=\dfrac{10^2}{1+8+27+64}=\dfrac{100}{100}=1\)

2: \(\left(2^3\right)^4-\left(2^6\right)^2=2^{12}-2^{12}=0\)

3: \(\dfrac{\left(-1\right)^3}{15}+\left(-\dfrac{2}{3}\right)^2:2\dfrac{2}{3}+\dfrac{5}{6}\)

\(=\dfrac{-1}{15}+\dfrac{4}{9}:\dfrac{8}{3}+\dfrac{5}{6}\)

\(=-\dfrac{1}{15}+\dfrac{5}{6}+\dfrac{12}{72}=-\dfrac{1}{15}+1=\dfrac{14}{15}\)