To raise a term with an exponent to another exponent, retain the base and multiply the exponents:

To multiply terms with radicals, multiply the coefficients and radicands separately:

4\( \sqrt{4} \) x 9\( \sqrt{5} \)
(4 x 9)\( \sqrt{4 \times 5} \)
36\( \sqrt{20} \)

Now we need to simplify the radical:

36\( \sqrt{20} \)
36\( \sqrt{5 \times 4} \)
36\( \sqrt{5 \times 2^2} \)
(36)(2)\( \sqrt{5} \)
72\( \sqrt{5} \)

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

The first few multiples of 2 are [2, 4, 6, 8, 10, 12, 14, 16, 18, 20] and the first few multiples of 10 are [10, 20, 30, 40, 50, 60, 70, 80, 90]. The first few multiples they share are [10, 20, 30, 40, 50] making 10 the smallest multiple 2 and 10 have in common.

To divide terms with radicals, divide the coefficients and radicands separately:

\( \frac{45\sqrt{12}}{9\sqrt{3}} \)
\( \frac{45}{9} \) \( \sqrt{\frac{12}{3}} \)
5 \( \sqrt{4} \)