This study notes covers Worked Example 3: Power of a Power within Index Laws for GCSE Mathematics. Revise Index Laws in Number for GCSE Mathematics with 14 exam-style questions and 22 flashcards. This topic shows up very often in GCSE exams, so students should be able to explain it clearly, not just recognise the term. It is section 9 of 14 in this topic. Use this study notes to connect the idea to the wider topic before moving on to questions and flashcards.
Worked Example 3: Power of a Power
Simplify: (2³)⁴
Solution
Using (aᵐ)ⁿ = aᵐⁿ
Multiply the indices: 3 × 4 = 12
Answer: 2¹²
Check: (2³)⁴ = 8⁴ = 4096 and 2¹² = 4096 ✓
Practice questions for Index Laws
Which of these is equivalent to a³ × a⁵?
Simplify a⁵ × a³
Quick recall flashcards
Division Law
aᵐ ÷ aⁿ = aᵐ⁻ⁿ
SUBTRACT the powers
Example: 5⁶ ÷ 5² = 5⁴
Zero Power Law
a⁰ = 1
ANY number to power 0 equals 1
(except 0⁰ which is undefined)
Examples: 5⁰ = 1, 100⁰ = 1