Higher November 2017 Paper 1 Q14
14. Simplify \(\sqrt[3]{64} \times 2^{-4} \times 4^{9}\).
Give your answer as a power of 2. [4]
| Scheme | Marks | Comments |
|---|---|---|
| \((\sqrt[3]{64} =)\ 2^{\frac{6}{3}}\) or \(2^2\) | B1 | |
| \((4^9 =)\ \left[2^2\right]^9\) or \(2^{18}\) | B1 | |
| \(2^{2-4+18}\) or equivalent | M1 | FT ‘their 18’ and ‘their 2’ providing both are positive Complete method required. |
| \(2^{16}\) | A1 | CAO |
Alternative method 1
| Scheme | Marks |
|---|---|
| \(\sqrt[3]{64} \times 4^9 = 4^{10}\) seen or implied | B1 |
| \((4^{10} =)\ \left[2^2\right]^{10}\) or \((2^{-4} =)\ 4^{-2}\) seen or implied | B1 |
| \(2^{20-4}\) or \(4^{10-2}\) or equivalent | M1 |
| \(2^{16}\) | A1 |
Alternative method 2
| Scheme | Marks |
|---|---|
| \((2^{-4} =)\ \dfrac{1}{16}\) seen or implied | B1 |
| \(\sqrt[3]{64} \times \dfrac{1}{16} = \dfrac{1}{4}\) seen or implied | B1 |
| \(4^{9-1}\) or equivalent | M1 |
| \(2^{16}\) | A1 |
| (4) |