2root(3)(4)*2root(3)(2) What is the value of the given expression? Choose 1 answer: (A) 2root(3)(6) (B) 4root(6)(8) (C) 8 (D) 16

Understand the expression: Understand the expression and the operation involved. We have the expression 2root(3)(4) * 2root(3)(2), which means we are multiplying two cube roots. The cube root of a number is the value that, when cubed, gives the original number. We will use the property of exponents that allows us to multiply the radicands (the numbers under the cube root) when the roots are of the same index.Multiply the radicands: Multiply the radicands under the cube root. Using the property of exponents for roots with the same index, we can combine the radicands: 2root(3)(4) * 2root(3)(2) = 2root(3)(4 * 2)Calculate the product of the radicands: Calculate the product of the radicands. Now we multiply the numbers under the cube root: 4 * 2 = 8 So, 2root(3)(4 * 2) = 2root(3)(8)Simplify the cube root: Simplify the cube root. The cube root of 8 is 2, because 2^3 = 8. Therefore: 2root(3)(8) = 2 * 2 = 4Check the answer choices: Check the answer choices. We have calculated the value to be 4, which is not listed in the answer choices. This suggests there might be an error in the calculation.

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$2\sqrt[3]{4} \cdot 2\sqrt[3]{2}$ $\newline$ What is the value of the given expression? $\newline$ Choose $1$ answer: $\newline$ (A) $2\sqrt[3]{6}$ $\newline$ (B) $4\sqrt[6]{8}$ $\newline$ (C) $8$ $\newline$ (D) $16$

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Math Problems

Algebra 1

Multiplication with rational exponents

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2\sqrt[3]{4} \cdot 2\sqrt[3]{2}

\newline

What is the value of the given expression?

\newline

Choose

1

answer:

\newline

(A)

2\sqrt[3]{6}

\newline

(B)

4\sqrt[6]{8}

\newline

(C)

8

\newline

(D)

16

Understand the expression: Understand the expression and the operation involved. $\newline$ We have the expression $2\sqrt[3]{4} \times 2\sqrt[3]{2}$ , which means we are multiplying two cube roots. The cube root of a number is the value that, when cubed, gives the original number. We will use the property of exponents that allows us to multiply the radicands (the numbers under the cube root) when the roots are of the same index.
Multiply the radicands: Multiply the radicands under the cube root. $\newline$ Using the property of exponents for roots with the same index, we can combine the radicands: $\newline$ $2\sqrt[3]{4} \times 2\sqrt[3]{2} = 2\sqrt[3]{4 \times 2}$
Calculate the product of the radicands: Calculate the product of the radicands. $\newline$ Now we multiply the numbers under the cube root: $\newline$ $4 \times 2 = 8$ $\newline$ So, $2\sqrt[3]{4 \times 2} = 2\sqrt[3]{8}$
Simplify the cube root: Simplify the cube root. $\newline$ The cube root of $8$ is $2$ , because $2^3 = 8$ . Therefore: $\newline$ $2\sqrt[3]{8} = 2 \times 2 = 4$
Check the answer choices: Check the answer choices. $\newline$ We have calculated the value to be $4$ , which is not listed in the answer choices. This suggests there might be an error in the calculation.