Higher June 2023 Paper 1 Q14
14
(a) Write \(\dfrac{1}{16}\) in the form \(4^n\) where \(n\) is an integer. (1)
(b) Work out the value of \(8^{\frac{5}{3}} - 9^{\frac{3}{2}}\) (3)
| Answer | Mark | Mark scheme |
|---|---|---|
| \(4^{-2}\) | B1 | for \(4^{-2}\) |
Additional guidance
Accept \(n = -2\)
| Answer | Mark | Mark scheme |
|---|---|---|
| 5 | M1 | for \(8^{\frac{5}{3}} = \left(\sqrt[3]{8}\right)^5\) or \(2^5\) or \(\sqrt[3]{8^5}\) or \(\sqrt[3]{32768}\) or \(9^{\frac{3}{2}} = \left(\sqrt{9}\right)^3\) or \(3^3\) or \(\sqrt{9^3}\) or \(\sqrt{729}\) |
| M1 | for correctly evaluating \(8^{\frac{5}{3}}\) or \(9^{\frac{3}{2}}\), eg 32 or 27 seen | |
| A1 | cao |