Exponents and roots

Learn what exponentiation means as repeated multiplication, evaluate small positive integer powers by hand, and predict the sign of a negative base raised to an even or odd exponent.

Learn the product rule for exponents - when multiplying powers with the same base, add the exponents - and apply it to expressions with numerical coefficients and multiple variables.

Learn three key exponent rules: the quotient rule for dividing powers with the same base, the power-of-a-power rule for raising a power to another power, and the power-of-a-product rule for distributing an exponent across factors.

Learn why any non-zero number raised to the power zero equals one, how negative exponents represent reciprocals, and how to simplify expressions by rewriting negative exponents as positive.

Learn what square roots are and how they relate to squaring, identify principal and negative roots, and estimate square roots of non-perfect squares.

Learn to split and combine square roots using the product and quotient rules for radicals.

Learn to simplify square roots by factoring out perfect squares, and rationalise expressions to remove radicals from the denominator.

Learn to rationalise a denominator with two terms involving square roots by multiplying by its conjugate, so the difference of squares clears the root.

Learn how fractional exponents connect to roots: the half-power $a^{1/2}$ equals $\sqrt{a}$, and more generally $a^{1/n}$ equals the $n$th root of $a$.

Learn how to evaluate general fractional exponents by combining roots and powers, and apply the product, quotient, and power rules to simplify expressions with fractional exponents.