To add or subtract terms with exponents, both the base and the exponent must be the same. In this case they are so add the coefficients and retain the base and exponent:

9x⁶ + 2x⁶
(9 + 2)x⁶
11x⁶

The least common multiple (LCM) is the smallest positive integer that is a multiple of two or more integers.

To simplify this fraction, first find the greatest common factor between them. The factors of 16 are [1, 2, 4, 8, 16] and the factors of 60 are [1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60]. They share 3 factors [1, 2, 4] making 4 their greatest common factor (GCF).

Next, divide both numerator and denominator by the GCF:

\( \frac{16}{60} \) = \( \frac{\frac{16}{4}}{\frac{60}{4}} \) = \( \frac{4}{15} \)

To add these fractions, first find the lowest common multiple of their denominators. The first few multiples of 8 are [8, 16, 24, 32, 40, 48, 56, 64, 72, 80] and the first few multiples of 12 are [12, 24, 36, 48, 60, 72, 84, 96]. The first few multiples they share are [24, 48, 72, 96] making 24 the smallest multiple 8 and 12 share.

Next, convert the fractions so each denominator equals the lowest common multiple:

\( \frac{2 x 3}{8 x 3} \) + \( \frac{3 x 2}{12 x 2} \)

\( \frac{6}{24} \) + \( \frac{6}{24} \)

Now, because the fractions share a common denominator, you can add them:

\( \frac{6 + 6}{24} \) = \( \frac{12}{24} \) = \(\frac{1}{2}\)

The factors of a number are all positive integers that divide evenly into the number. The factors of 16 are 1, 2, 4, 8, 16.