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To find the smallest possible values for A and B in a 10-digit number divisible by both 8 and 9, the last three digits (9B8) must be divisible by 8, and the sum of all digits must be divisible by 9. This leads to B=2 and A=3 as the smallest possible values.

The equation x^2 - 2x = 0 has two solutions, x = 0 and x = 2, not just x = 2.

The solution for b in the equation 2^(b^2+2) = 64 is b = 2.

To find 2^(m+n), solve for m and n in the equations 2^m = 1 and 2^n = 16, then substitute the values into the expression.

The expression 0^0 is considered an indeterminate form in calculus because different approaches to evaluating it yield different potential values. While some approaches suggest a value of 1 and others suggest 0, the limit does not have a single, well-defined value. In some contexts, like combinatorics, it is defined as 1 for convenience.

The magnitude of the given row vector is calculated, resulting in 3.

The determinant of the 3x3 matrix is calculated using the formula a(ei - fh) - b(di - fg) + c(dh - eg), resulting in a determinant of 0.

The multiplication of the two given matrices results in a 2x3 matrix with entries calculated by multiplying corresponding rows and columns of the matrices and summing the products.

The provided document details the simplification of algebraic fractions and the solution of algebraic expressions. Part 1 simplifies various rational expressions by factoring the numerators and denominators, canceling common factors. Part 2 involves adding, subtracting, and multiplying rational expressions, often requiring finding common denominators and simplifying the resulting expressions.

The equation 3^x - 2^x = 65 has a solution at x = 4.