Two powers of one number, divided
Halve a 64 cm rope. Keep halving. How long is it after five halvings?
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3⁵ ÷ 3² as a fraction. Step 1 of 4
3⁵ ÷ 3²as a fraction.- Two bottom 3s cancel two top 3s.
- Three 3s left:
3³. 3³= 27.
The rule
After five halvings the rope is 2 cm long.
Two powers of one base divide by cancelling factors. Cancelling removes a matching factor from the top and the bottom. The counts subtract. The base stays. 3⁵ ÷ 3² is 3³, because 5 − 2 = 3. That is 27.
- 64 is
2⁶, and each halving divides by 2. After five halvings:2⁶ ÷ 2⁵=2¹= 2 cm. 10⁴ ÷ 10¹=10³. One ten cancels, so 4 − 1 = 3.2⁶ ÷ 2²=2⁴. Two 2s cancel, so 6 − 2 = 4.
This works when the top count is bigger. Then at least one factor is left.