Emily claims that

Question

3^2/3*root(6,3^3)=3^(2)/(3)*3^3/6=3(6)/(18)=root(3,3)
Is Emily correct? Justify your answer.

Please upload a picture of your handwritten work below.

(3 points)

Answer 1

To justify whether Emily's claim is correct, let us simplify each step of her work.

Step 1: 3^(2/3) * root(6, 3^3)
The cube root of 3^3 is 3, so this expression becomes:
3^(2/3) * 3
= 3^(2/3+1)
= 3^(5/3)
= (3^5)^(1/3)
= 243^(1/3)
= root(3, 243)

Step 2: 3^(2)/(3) * 3^3/6
Let's evaluate each part of this expression separately.
3^(2)/(3) = (3^2)/(3) = 9/3 = 3
3^3/6 = (3^3)/(6) = 27/6 = 9/2
Multiplying these two parts, we get:
3 * (9/2) = 27/2

As we see, the expression in the first step is not equal to the expression in the second step, so Emily's claim is NOT correct.

Answer 2

Justify your answer and Simplify

Answer 3

Certainly!

To justify our answer, let's simplify each step of Emily's work and compare the results.

Step 1: 3^(2/3) * ∛(3^3)
We can simplify 3^(2/3) as follows:
3^(2/3) = (3^(1/3))^2 = ∛(3)^2 = (√3)^2 = 3.
So, the expression becomes:
3 * ∛(3^3) = 3 * ∛(27) = 3 * 3 = 9.

Step 2: 3^(2)/(3) * 3^3/6
We can simplify this expression separately:
3^(2)/(3) = (3^2)/(3) = 9/3 = 3.
3^3/6 = (3^3)/(6) = 27/6 = 4.5.
Multiplying these two parts, we get:
3 * 4.5 = 13.5.

Comparing the results:
In Step 1, the expression is equal to 9.
In Step 2, the expression is equal to 13.5.

Since 9 is not equal to 13.5, Emily's claim is NOT correct.

Therefore, Emily's claim is incorrect.