4400 Higher June 2009 Paper 4 Q22

(a) Each of the numbers \(x\), \(y\) and \(z\) is greater than 1 and less than 10
\(x \times 10^5 + y \times 10^4 = z \times 10^5\)
Find an expression for \(z\) in terms of \(x\) and \(y\).
Give your answer as simply as possible. (2)

(b) Each of the numbers \(3 \times 10^n\), \(4 \times 10^m\) and \(a \times 10^p\) is in standard form.\[\frac{3 \times 10^n}{4 \times 10^m} = a \times 10^p\] (3)