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Negative and Fractional Indices

Tuesday, 14 October 2025

maths year-1 pure-maths year-1-pure-maths chapter-1-algebraic-expressions bitesize

a^{\frac{1}{m}} = m a a^{\frac{n}{m}} = m a^{n} a^{-} m = \frac{1}{a ^{m}} a^{0} = 1

$a^\frac{n}{m} = \sqrt[m]{ a^n }$ as words

\frac{n}{m} = \frac{powering}{rooting}

Expanding $(\sqrt{ a }) ^ 3$

a^{\frac{3}{2}} = (a)^{3} = a \times a \times a \dots = a a

Simplifying $a^3 + a^6$

a^{3} + a^{6} \dots = a^{3} (1 + a^{3}) since \frac{a ^{6}}{a ^{3}} = a^{3}