CAIE IGCSE Mathematics Extended E1.7.2 Understand & use the rules of indices

Practise applying index laws to simplify powers, combine bases and link exponential notation to roots and curves.

Syllabus
2028–2030
Objective
E1.7.2
Level
Extended

Exam points

  • simplify expressions like (243y^10)^(3/5) by multiplying indices and rooting constants
  • write products of powers as a single power of 3, keeping terms involving n in the exponent
  • use index rules in y=c^x to find c from a point, then evaluate a negative power

E1.7.2 Understand and use the rules of indices question 1

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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