Key Equations

Key Equations

Rules of Exponents For nonzero real numbers $a$ and $b$ and integers $m$ and $n$
Product rule	$a^m\cdot a^n=a^{m+n}$
Quotient rule	$\frac{a^m}{a^n}=a^{m-n}$
Power rule	${\left(a^m\right)}^n=a^{m\cdot n}$
Zero exponent rule	$a^0=1$
Negative rule	$a^{-n}=\frac{1}{a^n}$
Power of a product rule	${\left(a\cdot b\right)}^n=a^n\cdot b^n$
Power of a quotient rule	${\left(\frac{a}{b}\right)}^n=\frac{a^n}{b^n}$

perfect square trinomial	${(x+a)}^2=(x+a)(x+a)=x^2+2ax+a^2$
difference of squares	$(a+b)(a-b)=a^2-b^2$

difference of squares	$a^2-b^2=(a+b)(a-b)$
perfect square trinomial	$a^2+2ab+b^2={(a+b)}^2$
sum of cubes	$a^3+b^3=(a+b)(a^2-ab+b^2)$
difference of cubes	$a^3-b^3=(a-b)(a^2+ab+b^2)$