Emily claims that 3^2/3x6√3^3=3^2/3x3^3/6=3^6/8=3√3
Is Emily correct? Justify your answer.
No, Emily is not correct. Let's simplify the given expression step by step.
3^2/3 * 6√3^3
= 3^2/3 * 6 * 3^(3/2) (since √3 = 3^(1/2))
= 3^(2/3) * 6 * 3^(3/2)
= 6 * 3^(2/3+3/2)
= 6 * 3^(4/6 + 9/6)
= 6 * 3^(13/6)
= 6 * (3^(6/6) * 3^(7/6))
= 6 * (3 * 3^(7/6))
= 18 * 3^(7/6)
Therefore, the correct simplified expression is 18 * 3^(7/6), not 3√3. Emily's claim is incorrect.