WAECMathematics2022

Simplify (2³)².

A16
B32
C64CORRECT
D128
AI
Toasta AI Explanation
Why the answer is C, and why the others tempt you.
**The reasoning** When you have a power raised to another power, like (2³)², you **multiply the exponents**. This is the **Power of a Power Rule**: (aᵐ)ⁿ = aᵐⁿ So (2³)² = 2³ˣ² = 2⁶ = 64 You can also think of it step-by-step: - First: 2³ = 8 - Then: (2³)² = 8² = 64 Either way, you get **64**. **Why the wrong options tempt you** - **16 (A)**: You might mistakenly do 2³⁺¹ = 2⁴ = 16, adding instead of multiplying the exponents. - **32 (B)**: This is 2⁵, which you'd get if you added the exponents wrong (3+2=5). - **128 (D)**: This is 2⁷. You might have made an arithmetic error or confused the operation entirely. The trap is **adding exponents** when you should **multiply** them for powers of powers. **Quick takeaway** Power to a power? **Multiply the exponents**: (aᵐ)ⁿ = aᵐⁿ — it's like saying "three, but twice" = six times total!
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