Category:Exponent Combination Laws
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This category contains pages concerning Exponent Combination Laws:
Let $a, b \in \R_{>0}$ be strictly positive real numbers.
Let $x, y \in \R$ be real numbers.
Let $a^x$ be defined as $a$ to the power of $x$.
Then:
Product of Powers
- $a^x a^y = a^{x + y}$
Power of Product
- $\paren {a b}^x = a^x b^x$
Negative Power
- $a^{-x} = \dfrac 1 {a^x}$
Power of Power
Let $x, y \in \R$ be real numbers.
Let $a^x$ be defined as $a$ to the power of $x$.
Then:
- $\paren {a^x}^y = a^{x y}$
Quotient of Powers
- $\dfrac{a^x} {a^y} = a^{x - y}$
Power of Quotient
- $\paren {\dfrac a b}^x = \dfrac {a^x} {b^x}$
Negative Power of Quotient
- $\paren {\dfrac a b}^{-x} = \paren {\dfrac b a}^x$
Pages in category "Exponent Combination Laws"
The following 22 pages are in this category, out of 22 total.
E
- Exponent Combination Laws
- Exponent Combination Laws/Also known as
- Exponent Combination Laws/Negative Power
- Exponent Combination Laws/Negative Power of Quotient
- Exponent Combination Laws/Positive Integers
- Exponent Combination Laws/Power of Power
- Exponent Combination Laws/Power of Power/Proof 1
- Exponent Combination Laws/Power of Power/Proof 2
- Exponent Combination Laws/Power of Product
- Exponent Combination Laws/Power of Quotient
- Exponent Combination Laws/Product of Powers
- Exponent Combination Laws/Product of Powers/Proof 1
- Exponent Combination Laws/Product of Powers/Proof 2
- Exponent Combination Laws/Product of Powers/Proof 2/Lemma
- Exponent Combination Laws/Rational Numbers