The Laws of Indices (Leaving Cert Mathematics): Flashcards

$a^p \cdot a^q = a^{p+q}$ (add exponents with same base).

$a^p / a^q = a^{p-q}$, subtract exponents with same base.

$(a^p)^q = a^{p*q}$ (multiply exponents together).

$(ab)^p = a^p \cdot b^p$ (distribute the exponent).

$(a/b)^p = a^p / b^p$ (distribute to numerator/denominator).

$a^0 = 1$ for any non-zero $a$.

$a^{-p} = 1/a^p$ (reciprocal of the base).

$a^{1/q} = \sqrt[q]{a}$, $a^{p/q} = (\sqrt[q]{a})^p$.

They simplify expressions and aid in calculations.

Convert roots into fractional exponents for simplification.