4MA0 Higher June 2017 Paper 4 Q22
22 \(m = 8 \times 10^{9n}\) where \(n\) is an integer.
Express \(m^{-\frac{1}{3}}\) in standard form.
Give your answer, in terms of \(n\), as simply as possible.
(3)
| Scheme | Marks |
|---|---|
e.g. \(\left(\dfrac{1}{8 \times 10^{9n}}\right)^{\frac{1}{3}}\) or \(\left(2 \times 10^{3n}\right)^{-1}\) or \(\dfrac{1}{\sqrt[3]{8 \times 10^{9n}}}\) or \(\left(\sqrt[3]{8 \times 10^{9n}}\right)^{-1}\) or \(\left(8^{\frac{-1}{3}} \times 10^{\frac{-9n}{3}}\right)\) or \(\left[\dfrac{1}{8^{\frac{1}{3}}}\text{ and }\dfrac{1}{\left(10^{9n}\right)^{\frac{1}{3}}}\right]\) or \(\left[2^{-1}\text{ and }(10^{3n})^{-1}\right]\) oe | M1 |
e.g. \(\dfrac{1}{2 \times 10^{3n}}\) or \(0.5 \times 10^{-3n}\) oe or \(\left[8^{\frac{-1}{3}} = 0.5\text{ and }(10^{9n})^{\frac{-1}{3}} = 10^{-3n}\right]\) oe | M1 |
| \(5 \times 10^{-3n - 1}\) | A1 |
| (3) | |
| (3 marks) |
Notes
M1: Correct first stage.
M1: For dealing with \(8^{-1/3}\) (shown as ½ or 0.5) and \((10^{9n})^{-1/3}\) shown as \(10^{-3n}\)
A1: \(5 \times 10^{-(3n + 1)}\)