00:01
All right, for this problem, we need to simplify 16 raised to the two -thirds power raised to the one -half power.
00:08
So we have to recognize first that when we have a power raised to another power, we can simplify that by multiplying those two powers together.
00:20
So we want to multiply two -thirds times one -half.
00:23
So we multiply across the top to get two, multiply across the bottom to get six.
00:29
So this can be rewritten as 16 to the 2 sixths, but this fraction can be reduced.
00:36
So that's going to be the same as 16 to the 1 third.
00:41
So whenever we're raising anything to a fractional power, we're really taking a root, a square root, a cube root, a fourth root, something like that.
00:52
And so the way we rewrite this is 16 is our base, the numerator is the exponent, and then we're under a radical and the denominator is the power of the radical.
01:05
So we're saying that we want the third root of 16 to the first power...