Grade 7 - Powers and Number Properties

Apply divisibility tests for 2, 3, 4, 5, 6, 8, 9, and 10; determine prime factorizations, greatest common factors, and least common multiples of positive whole numbers using factorization or lists. Interpret and write repeated multiplication in exponent notation and evaluate powers with whole-number bases and exponents, including powers of 10, the convention $a^0=1$ for nonzero bases, and the sign effects of even and odd exponents on negative bases while distinguishing $(-a)^n$ from $-a^n$. Recognize perfect squares from 0 through 144 and determine their principal whole-number square roots, while understanding that equations such as $x^2=49$ have both positive and negative integer solutions.