Evaluate. root(3)(-54)*root(3)((1)/(2))=

Identify cube roots: Identify the cube roots to be multiplied. We have two cube roots: the cube root of -54 and the cube root of 1/2. We need to multiply these two cube roots together.Simplify cube root of -54: Simplify the cube root of -54. The cube root of -54 can be simplified by finding a perfect cube that is a factor of 54. We know that 27 is a perfect cube (3^3) and is a factor of 54. So we can write -54 as -27 * 2. The cube root of -27 is -3, because (-3)^3 = -27.Simplify cube root of 1/2: Simplify the cube root of 1/2. The cube root of 1/2 cannot be simplified further because 1/2 is already in its simplest form. However, we can express it as the cube root of 1 divided by the cube root of 2.Multiply simplified cube roots: Multiply the simplified cube roots. Now we multiply the cube roots we found in Step 2 and Step 3. So we have (-3) * (cube root of 1/2).Calculate final answer: Calculate the final answer. Multiplying -3 by the cube root of 1/2 gives us -3 * (1/2)^(1/3). This is the final simplified form of the expression.

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Evaluate.

root(3)(-54)*root(3)((1)/(2))=

Evaluate. $\newline$ $\sqrt[3]{-54} \cdot \sqrt[3]{\frac{1}{2}}=$

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Grade 6

Multiply using the distributive property

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Q. Evaluate.

\newline

\sqrt[3]{-54} \cdot \sqrt[3]{\frac{1}{2}}=

Identify cube roots: Identify the cube roots to be multiplied. $\newline$ We have two cube roots: the cube root of $-54$ and the cube root of $\frac{1}{2}$ . We need to multiply these two cube roots together.
Simplify cube root of $-54$ : Simplify the cube root of $-54$ . The cube root of $-54$ can be simplified by finding a perfect cube that is a factor of $54$ . We know that $27$ is a perfect cube $(3^3)$ and is a factor of $54$ . So we can write $-54$ as $-27 \times 2$ . The cube root of $-27$ is $-54$ $0$ , because $-54$ $1$ .
Simplify cube root of $\frac{1}{2}$ : Simplify the cube root of $\frac{1}{2}$ . The cube root of $\frac{1}{2}$ cannot be simplified further because $\frac{1}{2}$ is already in its simplest form. However, we can express it as the cube root of $1$ divided by the cube root of $2$ .
Multiply simplified cube roots: Multiply the simplified cube roots. $\newline$ Now we multiply the cube roots we found in Step $2$ and Step $3$ . So we have $(-3) \times (\text{cube root of } \frac{1}{2})$ .
Calculate final answer: Calculate the final answer. $\newline$ Multiplying $-3$ by the cube root of $\frac{1}{2}$ gives us $-3 \times \left(\frac{1}{2}\right)^{\frac{1}{3}}$ . This is the final simplified form of the expression.