Question Video: Simplifying the Multiplication of Two Cube Roots | Nagwa Question Video: Simplifying the Multiplication of Two Cube Roots | Nagwa

Question Video: Simplifying the Multiplication of Two Cube Roots Mathematics • Second Year of Preparatory School

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Express ∛4 × ∛−16 in its simplest form.

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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.

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