Final answer:
Jude incorrectly squared the common base (1/2) when she should have added the exponents. The correct simplification of (1/2)² × 1/2 × (1/2)³ is (1/2)⁵, which equals 1/32.
Step-by-step explanation:
Jude made a common mistake while simplifying the expression (1/2)² × 1/2 × (1/2)³. Instead of combining the exponents correctly, Jude incorrectly assumed that raising the power of a power would simply entail squaring (1/8), thus ending up with (1/8)⁶ which equates to 1/262,144. However, the correct method to simplify the expression involves adding the exponents when multiplying the same base number. The correct simplification would be (1/2)⁵ because we have (1/2)² (twice), then multiplied by 1/2 (once), and then by (1/2)³ (thrice), so the sum of the exponents is 2+1+3=6. Therefore, (1/2)⁵ equals 1/32. Following the rules for powers and exponents ensures that we arrive at the correct mathematical solution.