- two examples of expanding the exponent are:
$3^4 = 3 \cdot 3 \cdot 3 \cdot 3 = 81$ and$2^{-3} = (\frac{1}{2})^3 = \frac{1}{2^3} = \frac{1}{2 \cdot 2 \cdot 2} = \frac{1}{8}$ - a root of a number involves a fractional exponent for example the quantity
$x^{\frac{1}{n}}$ is the nth root of$x$ - when multiplying powers of the same base add exponents togethor:
$x^a \cdot x^b = x^{a+b}$ - when dividing powers of the same base you subtract the exponents:
$\frac{x^a}{x^b} = x^a \div x^b = x^{a-b}$ - any number except zero when raised to the power of zero equals one:
$n^3 \div n^3 = n^{3-3} = n^0 = 1$ as long as$n \neq 0$ - the power of power is:
$(a^m)^p = a^{m \cdot p}$ for example$(2^3)^4 = 2^{3 \cdot 4} = 2^{12}$ - when raising two numbers to the same power their products and quotients obey simple rules:
$(x^n)(y^n) = (xy)^n$ and$\frac{x^n}{y^n} = (\frac{x}{y})^n$
- the equation to convert celsius to fahrenheit is:
$F = C \cdot \frac{9}{5} + 32$ - the equation of a unit circle is:
$x^2 + y^2 = 1$ - the relationship between sine and cosine is famously shown with the Pythagorean identity:
$\sin^2\theta + \cos^2\theta = 1$ $\tan\theta = \frac{\sin\theta}{\cos\theta}$ - absolute value or modulus of a complex number
$a + bi$ is$$|a + bi| = \sqrt{a^2 + b^2}$$ - in Boyle's law the product of pressure (P) and volume (V) is a constant number (k):
$P \cdot V = k$ which means that pressure is inversely proportional to the volume
