Evaluate. root(5)(-16)*root(5)(2)=

Problem Understanding: Understand the problem. We need to find the product of the fifth roots of -16 and 2. This means we will multiply the fifth root of -16 by the fifth root of 2.Radical Notation: Write the expression using radical notation. The expression is written as √[5](-16) * √[5](2), where √[5] denotes the fifth root.Properties of Radicals: Recall the properties of radicals. The product of two radicals with the same index can be combined into a single radical containing the product of the radicands (the numbers under the radical sign). So, √[5](-16) * √[5](2) = √[5](-16 * 2).Multiplying the Radicands: Multiply the radicands. Now we multiply -16 by 2 to get -32. So, √[5](-16) * √[5](2) = √[5](-32).Evaluating the Fifth Root: Evaluate the fifth root of -32. The fifth root of a negative number is negative if it is an odd root, which is the case here. However, -32 is not a perfect fifth power, so the fifth root of -32 cannot be simplified to an integer. The expression remains √[5](-32).

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Evaluate. $\newline$ $\sqrt[5]{-16} \cdot \sqrt[5]{2}=$

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Grade 6

Multiply using the distributive property

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Q. Evaluate.

\newline

\sqrt[5]{-16} \cdot \sqrt[5]{2}=

Problem Understanding: Understand the problem. $\newline$ We need to find the product of the fifth roots of $-16$ and $2$ . This means we will multiply the fifth root of $-16$ by the fifth root of $2$ .
Radical Notation: Write the expression using radical notation. $\newline$ The expression is written as $\sqrt[5]{-16} \times \sqrt[5]{2}$ , where $\sqrt[5]{}$ denotes the fifth root.
Properties of Radicals: Recall the properties of radicals. $\newline$ The product of two radicals with the same index can be combined into a single radical containing the product of the radicands (the numbers under the radical sign). So, $\sqrt[5]{-16} \times \sqrt[5]{2} = \sqrt[5]{-16 \times 2}$ .
Multiplying the Radicands: Multiply the radicands. $\newline$ Now we multiply $-16$ by $2$ to get $-32$ . So, $\sqrt[5]{-16} \times \sqrt[5]{2} = \sqrt[5]{-32}$ .
Evaluating the Fifth Root: Evaluate the fifth root of $-32$ . $\newline$ The fifth root of a negative number is negative if it is an odd root, which is the case here. However, $-32$ is not a perfect fifth power, so the fifth root of $-32$ cannot be simplified to an integer. The expression remains $\sqrt[5]{-32}$ .