1. Rules on Multiplying powers with same base:
Rule for multiplying powers,
\(n^a \times n^b = n^{(a+b)}\)
Example:
\(4^2 \times 4^4 = 4^{(2+4)} = 4^6\)
\(4^4 \div 4^2 = 4^{(4-2)} = 4^2\)
2.Power of Quoitent rule
\(\frac{m^{a}}{n^{a}} = {(\frac{m}{n})}^a\)
Example:
\(\frac{5^{2}}{6^{2}} = {(\frac{5}{6})}^2\)
3. Power of a power:
Rule for calculating a power of a power,
\((n^{a})^{b} = n^{ab}\)
Example:
\((4^{2})^{3} = 4^{2\times3} = 4^{6} = 4096\)
4. Power of a product rule:
Rule for calculating power of a product:
\(m^a \times n^a\) \(=\) \((m \times n)^a\)
Example:
\(5^2 \times 6^2\) \(=\) \((5 \times 6)^2\) \(=\) \(30^2\)