Higher June 2023 Paper 2R Q11
11 Express \(\left(\dfrac{m^6k^{10}}{25}\right)^{\frac{3}{2}}\;\) in the form \(\;\dfrac{m^ak^b}{c}\;\) where \(a\), \(b\) and \(c\) are integers to be found.
(2)
| Scheme | Marks |
|---|---|
| \(\dfrac{m^9k^{15}}{125}\) | B2 |
| (2) | |
| (2 marks) |
Notes
B2: oe for all 3 correct eg \(125^{-1}m^9k^{15}\) or \(\dfrac{1}{125}m^9k^{15}\)
Accept \(a = 9\), \(b = 15\) and \(c = 125\)
B1 for a quotient in the form of \(\dfrac{m^pk^q}{r}\) or a product in the form \(r^{-1}m^pk^q\) where 2 from \(p\) or \(q\) or \(r\) are correct
eg \(\dfrac{m^9k^{15}}{25}\) or \(125m^9k^{15}\)
Allow \(m^9k^{15}\) or \(\dfrac{m^9}{125}\) or \(125^{-1}m^9\) or \(\dfrac{k^{15}}{125}\) or \(125^{-1}k^{15}\) so long as not added to any other terms
Accept two from \(a = 9\) or \(b = 15\) or \(c = 125\)
Accept \(y125^{-1}m^9k^{15}\) or \(\dfrac{ym^9k^{15}}{125}\) where \(y\) is constant