How to Decode Negative and Fractional Exponents in Algebra
In short: Mastering indices is about understanding the relationship between powers and roots. This video explains how to manipulate negative and fractional exponents to simplify complex algebraic expressions.
The video breaks down two advanced rules of indices. Negative indices indicate a reciprocal: a term like x⁻² is rewritten as 1/x², moving the base to the denominator to make the exponent positive. Fractional indices represent roots and powers combined.
For a fraction like 3/2, the denominator represents the root (square root) and the numerator represents the power (cubing). While the order of operations can be swapped, the presenter recommends taking the root first to keep intermediate numbers smaller. For example, 25³⁄² is solved by taking the square root of 25 to get 5, then cubing it to reach 125.
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Sources
- Summary by Intellect · source: Laws Of Indices Part 2: Negatives & Fractions | Algebra | Maths | FuseSchool
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