emily claims that 3 2/3 times 6\sqrt{ }3^3 = 3 2/3 times 3 3/6 = 3 6/18 = 3\sqrt{ }3. Is emily correct? Explain your answer.
No, Emily is not correct.
First, let's simplify 3 2/3 times 6√(3)^3. This can be written as 11/3 times 6√(3)^3.
We know that 3 raised to the power of 3 is 27. Therefore, 6√(3)^3 is equal to 6√(3) * 6√(3) * 6√(3), which simplifies to 6 * 3 * 6√(3), or 108√(3).
Now, let's simplify 3 2/3 times 3 3/6. This can be written as 11/3 times 11/2.
To multiply fractions, we multiply the numerators and the denominators separately. The product of 11/3 times 11/2 is (11 * 11) / (3 * 2), which simplifies to 121/6.
Therefore, 3 2/3 times 6√(3)^3 is not equal to 3 2/3 times 3 3/6, making Emily's claim incorrect.