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CAIE IGCSE Mathematics Fractional and Negative Indices

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

Syllabus
2028–2030
Course
Mathematics 0580
Level
Extended

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

Covered syllabus points

E1.7.1 Understand and use indices (positive, zero, negative, and fractional).E1.7.2 Understand and use the rules of indices

E1.7 Indices I question 1

[Maximum number: 2]

Find the value of 642364^{\frac23}.

E1.7 Indices I question 2

[Maximum number: 2]

10f(x)=4−3x g(x)=x2+x h(x)=3x10 \quad \mathrm{f}(x)=4-3 x \quad \mathrm{~g}(x)=x^{2}+x \quad \mathrm{~h}(x)=3^{x}

1h(x)=9kx\frac{1}{h(x)}=9^{kx}

Find the value of k.

k=

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