Year 9: Evaluate the exponent of an exponent

This cheat sheet will help you understand and evaluate expressions with exponents of exponents. It’s a crucial concept for Year 9 Algebra!

What is an Exponent of an Exponent?

When you have an expression like x^y, this means ‘x’ raised to the power of ‘y’. If you have an expression like (x^y)^z, you need to understand how to evaluate it correctly.

The Rule

The key rule is: (x^y)^z = x^{(y * z)}

In other words, to raise a power to another power, you multiply the exponents.

Examples

• (x²)³ = x^{(2 * 3)} = x⁶
• (2³)² = 2^{(3 * 2)} = 2⁶ = 64
• (a⁴)² = a^{(4 * 2)} = a⁸

Important Note

Make sure you simplify your expression before applying the rule. Don’t just multiply the bases; you *must* multiply the exponents.