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 n-th 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 n-th 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.