CAIE IGCSE Mathematics Extended E1.7 Indices I Questions

Practise evaluating fractional and negative indices, rewriting terms with a common base and simplifying algebraic powers using index laws.

Exam points

evaluate a fractional index by applying the denominator as a root and numerator as a power
use a negative index to take the reciprocal before evaluating the remaining power or root
rewrite terms with a common base and combine exponents to simplify or solve an indexed relation

[Maximum number: 2]

Find the value of $64^{\frac23}$ .

[Maximum number: 2]

Simplify fully.
$\left(243y^{10}\right)^{\frac35}$

$27y^6$
final answer

B1 for $ky^6$ or $27y^k$ as final answer or correct answer seen and spoilt

[Maximum number: 2]

Find the value of

$125^{\frac{2}{3}}$ .

25 cao

M1 for $(\sqrt[3]{125})^2$ or $\sqrt[3]{125^2}$ or $(5^3)^{2/3}$
or B1 for $\sqrt[3]{125}=5$

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