Video Transcript
Express the cube root of four
multiplied by the cube root of negative 16 in its simplest form.
In order to answer this question,
we first recall that for any two real numbers 𝑎 and 𝑏, the cube root of 𝑎
multiplied by the cube root of 𝑏 is equal to the cube root of 𝑎 multiplied by
𝑏. This means that the cube root of
four multiplied by the cube root of negative 16 is equal to the cube root of four
multiplied by negative 16. Four multiplied by negative 16 is
negative 64. So our expression simplifies as
shown. Next, we note that negative four
cubed is equal to negative 64. And as such, the cube root of
negative 64 is negative four.
