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CAIE IGCSE Mathematics 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
Course
Mathematics 0580
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

[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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