Higher June 2019 Paper 1 Q23
23 Simplify \(\qquad 8^4 \div 32^{\frac{2}{5}}\)
Give your answer in the form \(\quad 2^m \quad\) where \(m\) is an integer. [3 marks]
| Answer | Mark | Comments |
|---|---|---|
| Alternative method 1 | ||
| \((8^4 =)\ (2^3)^4\) or \(2^{12}\) or \(\left(32^{\frac{2}{5}} =\right) (2^5)^{\frac{2}{5}}\) or \(2^2\) | M1 | |
| \(2^{12}\) and \(2^2\) | M1dep | or calculation in the form \(2^a \div 2^b\) where \(a - b = 10\) \(2^c \times 2^d\) where \(c + d = 10\) |
| \(2^{10}\) | A1 | Accept \(m = 10\) |
| Alternative method 2 | ||
| \((8^4 =)\ 4096\) or \(\left(32^{\frac{2}{5}} =\right) 4\) | M1 | |
| 1024 | M1dep | |
| \(2^{10}\) | A1 | Accept \(m = 10\) |
Additional guidance
Note that 1024 from \(32 \times 32\) scores 2 marks if 1024 is their final numerical answer
However, if they then try to find \(\sqrt[5]{1024}\) they are clearly processing \(\left(32^{\frac{2}{5}} =\right)\), so this would only score 0 marks without further work
If a numerical method and an index method are both attempted and an incorrect answer is given, award up to M1M1 from the better method