Find \(A\) and \(B\)  if  \({\left( {3.01 \times {{10}^4}} \right)^2} \times \left( {1.1 \times {{10}^{ – 5}}} \right) = A \times {10^B}\)   in scientific notation with two significant figures.

If \({u_{10}} = 100\)  and  \({u_{15}} = 175\),   find \({u_{100}}\) of the arithmetic sequence.

Consider the geometric sequence $k + 3,k,4, \cdots $.   Find the positive value of \(k \).

Find the principal that will grow to \($5000\) in 4 years, if interest is compounded quarterly at 8% per annum, correcting to the nearest cent.

A car was purchased for \($74000\) and depreciated at 5% each half-year.   Find its value after four years,   correcting to the nearest cent.

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

Find the value of \(3{x^0} + 2{y^0}\).

Write \(\dfrac{1}{{{3^{2 – x}}}}\) in non-fractional form.

Factorise \({9^x} + 4 \times {3^x} – 5\).

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