Find \(A\) and \(B\)  if  \(\left( {2.2 \times {{10}^3}} \right) \times \left( {1.8 \times {{10}^5}} \right) = A \times {10^B}\)   in scientific notation with two significant figures.

If \({t_{10}} = – \dfrac{1}{2}\)  and  \({t_{13}} = \dfrac{3}{4}\),   find \({t_{100}}\) of the arithmetic sequence.

A geometric sequence has \({u_2} = – 6\) and \({u_5} = 162\). Find its general term.

Given \(2.1444 \cdots = \dfrac{a}{{90}}\),   find  \(a \).

Find \(x\) and \(y\), if \(24 \times {2^3} \times {3^2} = {2^x}{3^y}\).

Find the value of \({\left( {{5^0} + {6^1} + {7^2}} \right)^0}\).

Solve   \({4^x} – 6 \times {2^x} + 8 = 0\).  There could be more than one answer.

Solve \({\log _{10}}x = – 5\), correcting to one significant figures.

Solve \({8^x} – 5 \times {4^x} = 0\), correct to 2 significant figures.

Find the constant term in the expansion of \({\left( {x + \dfrac{2}{{{x^2}}}} \right)^{15}}\).