What is the smallest integer greater than 10 that is both a perfect square and a perfect cube?
To find the smallest integer that satisfies both conditions, I need to think of the smallest possible exponents for the square and the cube roots. A perfect square means that the integer is the result of raising some other integer to the power of 2. A perfect cube means that the integer is the result of raising some other integer to the power of 3. So I need to find the smallest integer that is the result of raising some other integer to the power of 6, since 6 is the least common multiple of 2 and 3. This way, I can take both the square root and the cube root of the integer and get another integer. The smallest integer that I can raise to the power of 6 and get a result greater than 10 is 2. So the smallest integer that is both a perfect square and a perfect cube is 2^6, which is 64. 