#NumberAndAlgebra #Path #Adv >[!info]- [Indices B (Path) | NSW Curriculum Website](https://curriculum.nsw.edu.au/learning-areas/mathematics/mathematics-k-10-2022/content/stage-5/fa24d5bd5b) >- MA5-IND-P-01 applies the index laws to operate with algebraic expressions involving negative-integer indices ## 📖 Prior Knowledge | Content | Prior knowledge | Used for | | -------------------------- | -------------------------------------- | ------------------------------------- | | [[Indices A]] | - negative indices with numerical base | - negative indices with variable base | ## [[Apply index laws to algebraic expressions involving negative-integer indices.pdf]] - Apply index notation, patterns and index laws to establish $a^-1=\frac{1}{a}$, $a^{-2}=\frac{1}{a^2}$, $a^{-3}=\frac{1}{a^3}$, and $a^{-n}=\frac{1}{a^n}$ - Represent expressions involving negative-integer indices as expressions involving positive-integer indices and vice versa - Apply the index laws to simplify algebraic products and quotients involving negative-integer indices - Describe and use $x^{-1}$ as the reciprocal of $x$ and generalise this relationship to expressions of the form $(\frac{a}{b})^{-1}$ - Use knowledge of the reciprocal to simplify expressions of the form $(\frac{a}{b})^{-n}$