x

What indices are telling you

One helpful way to calculate $a^{-m/n}$ is:

Negative sign: take the reciprocal.
Denominator $n$ : take the $n$ th root.
Numerator $m$ : raise to the power $m$ .

So

a^{-m/n}=\frac{1}{(\sqrt[n]{a})^m}=\frac{1}{\sqrt[n]{a^m}}

Example:

32^{-2/5}=\frac{1}{(\sqrt[5]{32})^2}=\frac{1}{2^2}=\frac{1}{4}

Fractional and Negative Indices Lesson

IGCSE
Maths
Fractional and Negative Indices

Step-by-step lessons covering Oxford AQA IGCSE Maths Fractional and Negative Indices for Core and Extended tier. Each lesson works through exam-style questions in Paper 1 and Paper 2 (Core: 1C and 2C; Extension: 1E and 2E) format. Since content from any part of the specification can appear on either paper, keep number and algebra fluency sharp throughout the course rather than leaving it until near the exam.

Lessons

x

What indices are telling you

One helpful way to calculate $a^{-m/n}$ is:

Negative sign: take the reciprocal.
Denominator $n$ : take the $n$ th root.
Numerator $m$ : raise to the power $m$ .

So

a^{-m/n}=\frac{1}{(\sqrt[n]{a})^m}=\frac{1}{\sqrt[n]{a^m}}

Example:

32^{-2/5}=\frac{1}{(\sqrt[5]{32})^2}=\frac{1}{2^2}=\frac{1}{4}

Fractional and Negative Indices Lesson

IGCSE
Maths
Fractional and Negative Indices

Step-by-step lessons covering Oxford AQA IGCSE Maths Fractional and Negative Indices for Core and Extended tier. Each lesson works through exam-style questions in Paper 1 and Paper 2 (Core: 1C and 2C; Extension: 1E and 2E) format. Since content from any part of the specification can appear on either paper, keep number and algebra fluency sharp throughout the course rather than leaving it until near the exam.