4400 Higher June 2008 Paper 4 Q7

(a) Write \(3^8 \times 3^6\) as a power of 3 (1)

(b) Write \(\dfrac{7^5}{7^2}\) as a power of 7 (1)

(c) \[\frac{5^n \times 5^3}{5^7} = 5^2\]Find the value of \(n\). (2)

(d) \(A = 2^3 \times 3^4 \times 5^{16}\)
\(B = 2^5 \times 3 \times 7^{12}\)
Find the Highest Common Factor of \(A\) and \(B\). (2)