Powers and Roots
Powers and Roots

Understand the rules of indices: When multiplying terms with the same base, add the exponents. When dividing, subtract the exponents. And, when a term is raised to a power, multiply the exponents.

Learn to simplify expressions using the laws of indices. For example, a^m * a^n equals a^(m+n), or (a^m)^n equals a^(mn).

Become familiar with fractional and negative indices. Recall that a^(n) = 1/(a^n) and a^(1/n) is the nth root of a.

Recognize that square roots, cube roots, and other radicals can also be written using fractional indices. For instance, √a can be rewritten as a^(1/2) and 3√a as a^(1/3).

Master the skills of squaring and cubing numbers, as well as finding square roots and cube roots.

Grasp how to solve equations involving powers and roots. Using strategies such as isolating the variable, taking the square root of both sides, or employing the quadratic formula.

Appreciate that the square root of a number has both a positive and negative solution. For example, the square root of 9 is both 3 and 3.

Remember to simplify radical expressions with variables. For instance, √(x^2) can be simplified to x . 
Practice factoring using the difference of squares and perfect square trinomials, which often involve roots.

Learn to use the power of a product and the power of a quotient rules. These state that (ab)^n equals a^n * b^n and (a/b)^n equals (a^n)/(b^n) respectively.

Understand rational exponents and how they relate to roots. For example, realise that a^(m/n) equals the nth root of a^m.

Apply the laws of exponentials to simplify problems and equations.

Practice equations containing surds or irrational numbers.
 Lastly, consistently review and practise these concepts using a variety of problems to enhance understanding and proficiency.