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Updated Mar 23, 2026

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1 page

Understanding the Rules of Indices

Leah Mc conville

@eahcconville_akjyell

Indices (or powers) are everywhere in maths, from basic calculations... Show more

$rules of indices rule 1 $a^m x a^n = a^{m+n}$ when muitiplying, add powers Fule 2 $\frac{a^m}{a^n} = a^{m-n}$ when dividing, subtract powe$

Rules of Indices

Ever wondered why $2^3 \times 2^2 = 2^5 $and not$ 2^6$? The rules of indices make working with powers straightforward once you know the patterns.

When multiplying terms with the same base, you add the powers: $a^m \times a^n = a^{m+n}$ . For dividing, you subtract the powers: $\frac{a^m}{a^n} = a^{m-n}$ . Think of it as keeping track of how many times you're multiplying the base number.

Power of a power means you multiply the indices: $(a^m)^n = a^{m \times n}$ . Two special cases to remember: $a^1 = a$ (power of 1 doesn't change anything) and $a^0 = 1$ (any number to the power of 0 equals 1).

The trickiest rules involve negative and fractional powers. A negative power like $a^{-m} = \frac{1}{a^m}$ means "flip it to make it positive". Fractional powers represent roots: $a^{\frac{1}{m}} = \sqrt[m]{a}$ .

Quick Check: Try $3^2 \times 3^4 $. Add the powers:$ 3^{2+4} = 3^6 = 729$

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101

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Updated Mar 23, 2026

•

1 page

Understanding the Rules of Indices

Leah Mc conville

@eahcconville_akjyell

Indices (or powers) are everywhere in maths, from basic calculations to complex equations. Learning these seven essential rules will give you the tools to tackle any indices problem with confidence.

$rules of indices rule 1 $a^m x a^n = a^{m+n}$ when muitiplying, add powers Fule 2 $\frac{a^m}{a^n} = a^{m-n}$ when dividing, subtract powe$

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Rules of Indices

Ever wondered why $2^3 \times 2^2 = 2^5 $and not$ 2^6$? The rules of indices make working with powers straightforward once you know the patterns.

Quick Check: Try $3^2 \times 3^4 $. Add the powers:$ 3^{2+4} = 3^6 = 729$