UNIT OVERVIEW

This unit builds on the exponent work you did in Grade 10. You learned about integer exponents like $x^2$ and $x^{-3}$. Now you will work with fractional exponents and discover how exponents connect to roots.

The key idea: $x^{\frac{1}{2}}$ is another way of writing $\sqrt{x}$.

By the end of this unit, you will be able to:

• Apply the laws of exponents to expressions with rational (fractional) exponents
• Convert between exponential form and surd (root) form
• Simplify expressions containing surds
• Rationalise denominators
• Solve equations involving exponents and surds

Where you will use these skills:

• Finance: Compound interest uses exponents. Understanding fractional exponents helps you calculate growth over partial periods.
• Science: Drug dosages and radioactive decay use exponential formulas.
• Construction: The diagonal of a 1 m × 1 m tile is $\sqrt{2}$ metres—a surd that appears often in building calculations.

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