Higher November 2017 Paper 1 Q30
30
(a) Work out the value of \(\quad 81^{-\frac{1}{4}}\) [2 marks]
(b) Write \(\quad 16 \times 8^{2x} \quad\) as a power of 2 in terms of \(x\). [3 marks]
| Answer | Mark | Comments |
|---|---|---|
| \(\dfrac{1}{81^{\frac{1}{4}}}\) or \(\dfrac{1}{\sqrt[4]{81}}\) or \(\sqrt[4]{\dfrac{1}{81}}\) or \(3^{-1}\) or \(9^{-\frac{1}{2}}\) or \(81^{\frac{1}{4}} = 3\) or \(\sqrt[4]{81} = 3\) or \(3^4 = 81\) | M1 | |
| \(\dfrac{1}{3}\) | A1 |
Additional guidance
| 3 without \(81^{\frac{1}{4}}\) or \(\sqrt[4]{81}\) | M0A0 |
| Answer | Mark | Comments |
|---|---|---|
| Alternative method 1 | ||
| (16 =) \(2^4\) or \(\left(2^3\right)^{2x}\) or \(2^{6x}\) | M1 | oe with consistent base 2 |
| (16 =) \(2^4\) and \(\left(2^3\right)^{2x}\) or \(2^{6x}\) | M1dep | |
| \(2^{4 + 6x}\) or \(2^{2(2 + 3x)}\) | A1 | |
| Alternative method 2 | ||
| (\(\left(4 \times 8^x\right)^2 =\)) \(\left(2^2 \times 2^{3x}\right)^2\) | M1 | |
| \(\left(2^{2 + 3x}\right)^2\) | M1dep | |
| \(2^{4 + 6x}\) or \(2^{2(2 + 3x)}\) | A1 | oe index |