1990 年

$(a^{2n})^3=$

$\dfrac{1-\dfrac{x-y}{x+y}}{1-\dfrac{x+y}{x-y}}=$

If $x=\dfrac{ab+1}{a-b}$, then $b=$

If $f(n)=\dfrac{1}{2}n(n-1)$, then $f(n+1)-f(n)=$

If $2=10^p$, $3=10^q$, express $\log\dfrac{1}{6}$ in terms of $p$ and $q$.

Let $a>b>0$. If $a$ and $b$ are respectively the $1^{\text{st}}$ and $2^{\text{nd}}$ terms of a geometric progression, the sum to infinity of the progression is

$a^3+8a^{-3}=$

If $p$ and $q$ are the roots of the equation $x^2-x+3=0$, then $(2^{p-2})(2^{q-2})=$

If $a:b=3:4$ and $b:c=2:5$, then $a^2:c^2=$

If 1 U.S. dollar is equivalent to 7.8 H.K. dollars and 1000 Japanese yen are equivalent to 53.3 H.K. dollars, how many Japanese yen are equivalent to 50 U.S. dollars?