Question

I WILL FAN AND MEDAL!!!!!!!!!!
Compare and Contrast: Below are two expressions. Simplify each and then choose the statement that is true.

Expression #1(3d)3(d)
Expression #2 (3d2)2

The exponents in Expression #1 are greater than the exponents of Expression #2.

The exponents on Expression #2 are greater than the exponents of Expression #1.

The exponents of Expression #1 are the same as the exponents of Expression #2.

The relationship cannot be determined with the given information.

Answer 1

Expression 1: \((3d^3)(d) \)

Expression 2: \( (3d^2)^2 \)

Did I understand both expressions correctly?

Answer 2

Yup you did @mathstudent55

Answer 3

Let's simplify each one:

1. \( (3d^3)(d) = 3d^3 \times d^1 = 3d^4\)

2. \((3d^2)^2 = 3^2 \times (d^2)^2 = 9 d^{2 \times 2} = 9 d^4 \)

Answer 4

Ok yes correct i see where your going

Answer 5

Wait. Isn't Expression 1:
\( (3d)^3 d \) ?

Answer 6

Yeah expression 1 is that

Answer 7

I originally put the parentheses in the wrong place.
1. \( (3d)^3 d = 3^3 d^3 d = 27 d^4 \)

Answer 8

Lol Ok I see what you mean

Answer 9

So what does that mean @mathstudent55

Answer 10

I'm not sure what they mean with the choices.
In the end, the exponent of d is 4 in either expression.
If that's what they mean then the exponents are equal.
That means choice C.

On the other hand, Expression 2 ends up with 9 which is \(3^2 \) and Expression 1 ends up with 27 which is \( 3^3 \), so here exponent 3 is greater than exponent 2.

Since the numbers can be written as 27 and 9 with no exponents, maybe they mean choice C, but I am not sure because I don't quite understand what they are asking.