00:03
Okay, and problem number 92, we want to use the product rule here to simplify the square of 150 m to the ninth and to the third.
00:13
And the product rule just says you can split the square root of a product of factors into a product of separate square roots.
00:23
So for us, that means we write this as the square root of 150 times the square root of m to the ninth, times the squared of into the third.
00:36
And then, of course, we're going to simplify each of these separately, and then just multiply them back together.
00:43
So the biggest perfect square that goes into 150 is 25.
00:48
So applying the product rule again, we write square root of 150 as the square root of 25 times the square root of six, and that is, of course, five square to six.
01:01
Now remember, for the variable ones, you're just going to divide the exponents by the root...