Power up to 1000 Find $x+y$, where $2^x\times5^y=1000$ Age 14 to 16 Challenge level Exploring and noticing Working systematically Conjecturing and generalising Visualising and representing Reasoning, convincing and proving Being curious Being resourceful Being resilient Being collaborative Problem Student Solutions Problem Find $x+y$, where $2^x\times5^y=1000$This problem is taken from the World Mathematics Championships Student Solutions Answer: $6$Index laws$1000=103=(2×5)3=23×53$So $x=3$ and $y=3$, so $x+y=6$.Calculating directly$1000=103=10×10×10=(2×5)×(2×5)×(2×5)=2×2×2×5×5×5=23×53$So $x=3$ and $y=3$, so $x+y=6$.