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. Also, the answer is not "emily is correct." so please explain why she is wrong.
Emily is incorrect.
To solve the equation properly, we need to follow the correct order of operations.
First, let's evaluate 3 2/3 times 6√3^3.
3 2/3 times 6√3^3 = 3 2/3 times 6 × 3√3
Now, let's simplify the equation further using the order of operations.
3 2/3 times 6 × 3√3 = 11/3 times 6 × 3√3
To multiply fractions, we multiply the numerators together and the denominators together.
11/3 times 6 = 66/3 = 22
Therefore, we have:
22 × 3√3
Now we can simplify the expression.
22 × 3√3 = 66√3
So, the correct answer is 66√3, not 3√3 as Emily claimed.