4MA0 Higher January 2016 Paper 3R Q13

EdexcelHigherOld spec5 marksIndices

(a) Simplify \(\left(4h^{\frac{2}{3}}\right)^3\) (2)

\[\frac{a\sqrt{a}}{\sqrt[3]{a^2}} = a^k\]

(b) Work out the value of \(k\). (3)

Scheme	Marks
\(64h^2\)	B2
	(2)

Mark scheme (b)

Scheme	Marks
\(\dfrac{a \times a^{\frac{1}{2}}}{a^{\frac{2}{3}}}\) or \(\dfrac{a^{\frac{3}{2}}}{a^{\frac{2}{3}}}\)	M1
\(a^{\left(1 + \frac{1}{2} - \frac{2}{3}\right)}\) or \(k = \left(1 + \tfrac{1}{2} - \tfrac{2}{3}\right)\) oe or \(1 + \tfrac{1}{2} = k + \tfrac{2}{3}\) oe	M1
\(\dfrac{5}{6}\)	A1
	(3)

M1: For \(\sqrt{a} = a^{\frac{1}{2}}\) or \(a\sqrt{a} = a^{\frac{3}{2}}\) or \(\sqrt[3]{a^2} = a^{\frac{2}{3}}\)

M1: For \(a^{\left(1 + \frac{1}{2} - \frac{2}{3}\right)}\) or \(k = \left(1 + \tfrac{1}{2} - \tfrac{2}{3}\right)\)

A1: oe
Accept \(0.8\dot{3}\)