The Laws of Indices (Leaving Cert Mathematics): Flashcards

Shows how many times a number is multiplied by itself

$2$ (the number being multiplied)

$3$ (how many times to multiply the base by itself)

$a^{m+n}$ (add the indices)

$a^{m-n}$ (subtract the indices)

$a^{m×n}$ (multiply the indices)

$a^n × b^n$ (each factor raised to power)

$1$

$\frac{1}{a^n}$ (reciprocal with positive power)

$\sqrt[n]{a}$ (the $n$-th root of $a$)

$(\sqrt[n]{a})^m$ (take root, then raise to power)

Undefined

$4$ ($\sqrt[3]{8} = 2$, then $2^2 = 4$)