Year 10: Rational indices

Rational indices allow you to express roots as powers. Essentially, a^b/c means a raised to the power of b/c.

Key Concepts

• Simplifying Roots:a^b/c = (a^b)^1/c or (a¹)^b/c
• Example:x^(1/2) = √x (square root of x)
• Negative Indices:a^-n = 1 / aⁿ
• Example:x^-2 = 1 / x²

Rules

• Power of a Power: (a^m)ⁿ = a^mn
• Product of Powers:a^m * aⁿ = a^m+n
• Quotient of Powers:a^m / aⁿ = a^m-n

Practice

Remember to simplify fully. For example, x^(3/4) = (x³)^1/4 = (x¹)^3/4 = √[4]x = √[4]x