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Algebra · Laws of indices

05:18

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Rewrite each term with a common base, then use a^m × a^n = a^{m+n}.

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2:34 / 05:18
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1.1 Laws of Indices

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←  Back to Chapter 1: Algebra and Functions

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Pure Mathematics · Algebra and Functions

Laws of Indices

The laws of indices provide the algebraic rules for working with powers. These rules apply for all rational exponents.

Laws of Indices
am×an=am+na^m \times a^n = a^{m+n}am÷an=am−na^m \div a^n = a^{m-n}(am)n=amn(a^m)^n = a^{mn}a0=1a^0 = 1

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Chapter 7 · The chain rule

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Interactive lesson · Worked example

Differentiate a composite function

Differentiate the outer function first, keep the inner expression unchanged, then multiply by the inner derivative.

sin⁡(3x2+1)→6xcos⁡(3x2+1)\sin(3x^2+1)\rightarrow6x\cos(3x^2+1)

Follow the two layers

Outer function

sin⁡(u)→cos⁡(u)\sin(u)\rightarrow\cos(u)

Inner function

u=3x2+1→6xu=3x^2+1\rightarrow6x

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