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Rules of exponents
- 6.1 "Rules of exponents"
- Product Rule: a⌃m a⌃n = a⌃m+n
- Example: x⌃2 x⌃3 = x⌃2+3
- Example: x⌃2 x⌃3 = x⌃2+3
- Quotient Rule: a⌃m/a⌃n = a⌃m−n
- Example: y⌃2/y = y⌃2−1
- Example: y⌃2/y = y⌃2−1
- Negative Exponent Rule: a⌃−m = 1/a⌃m
- Example: y⌃−3 = 1/y⌃3
- Example: y⌃−3 = 1/y⌃3
- Zero Exponent Rule: a⌃0 = 1
- Example: x⌃0 = 1
- Example: x⌃0 = 1
- Raising a Power to a Power: (a⌃m)⌃n = a⌃mn
- Example: (x⌃2)⌃6 = x⌃2 6 = x⌃12
- Example: (x⌃2)⌃6 = x⌃2 6 = x⌃12
- Raising a Product to a Power: (ab)⌃m = a⌃m b⌃m
- Example: (yx)⌃4 = y⌃4 x⌃4
- Example: (yx)⌃4 = y⌃4 x⌃4
- Raising a Quotient to a Power: (a/b)⌃m = a⌃m/b⌃m
- Example: (x/y)⌃2 = x⌃2/y⌃2
- Example: (x/y)⌃2 = x⌃2/y⌃2
- Product Rule: a⌃m a⌃n = a⌃m+n
- 6.2 "Rational Exponents"
- Exponential Form of m√a is: n√a
= a⌃1/n
- Example: 3√x⌃11 = x⌃11/3
- Example: 3√x⌃11 = x⌃11/3
- Exponential Form of n√a⌃m is:
n√a⌃m = (n√a)⌃m = a⌃m/n
- Example: 4√8⌃7 x⌃21 y⌃14 = (4√8x⌃3 y⌃2)⌃7 = (8x⌃3 y⌃2)⌃7/4
- Example: 4√8⌃7 x⌃21 y⌃14 = (4√8x⌃3 y⌃2)⌃7 = (8x⌃3 y⌃2)⌃7/4
- Exponential Form of m√a is: n√a
= a⌃1/n
- 6.3 "Simplifying radicals"
- Product Rule for Radicals:n√a n√b = n√ab
- Example: √2 √5 = √10
- Example: √2 √5 = √10
- Quotient Rule for Radicals: n√a/n√b = n√a/b
- Example: √18/√3 = √18/3 = √6
- Example: √18/√3 = √18/3 = √6
- Product Rule for Radicals:n√a n√b = n√ab
- Usefull knowledges: here; "" is a multiplying sign.
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