Indices (Powers)
Follow index laws when working with powers. Use these to simplify expressions with exponents.
\(a^m \times a^n = a^{m+n}\)
\(\dfrac{a^m}{a^n} = x^{m-n}\)
\((a^m)^n = a^{mn}\)
\(a^{-1} = \dfrac{1}{a}\)
\(a^0 = 1 \quad \text{(for } a \ne 0\text{)}\)
Example
Example:
\( 2^2 \times 2^3 \)
\( = 2^{2+3} = 2^5 \)
\( = 32 \)
Practice
Write \( \dfrac{2^4 \times 2^3}{2^2} \) in the form \( 2^n \), where \( n \) is an integer.
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