5. Match each ⭐ with a 💎 .

Question

A card sort is on the screen. To start dragging a card, Tab to it and press M to mark it. Next, Tab to the card where you want to drop, and press J to join the two cards together. To unjoin the selected card from a group, press U.
3x−2 💎

1
x​ ⭐

3
x4​ ⭐

y3
x2​ ⭐

x2y−3 💎

x0 💎

x−2y3 💎

x−1 💎

x−3 💎

1
x3​ ⭐

3x−4 💎

3
x2​ ⭐

1 ⭐

To attach cards, drag it on TOP of each other until you see them CONNECT.

To detach, drag the BOTTOM card away.

x2
y3​

Answer 1

To match each starred cards (⭐) with diamond cards (💎), we need to look for equivalent algebraic expressions based on exponents of \( x \) and \( y \).

Here’s how we can match them:

1. \( \frac{1}{x} \) (⭐) can be matched with \( x^{-1} \) (💎) because \( \frac{1}{x} = x^{-1} \).

2. \( \frac{3}{x^4} \) (⭐) can be matched with \( 3x^{-4} \) (💎) for the same reason: \( \frac{3}{x^4} = 3x^{-4} \).

3. \( y^3x^2 \) (⭐) can be matched with \( x^2y^3 \) (💎) because these two expressions are equivalent regardless of the order (commutative property of multiplication).

4. \( x^{-2}y^3 \) (⭐) can be matched with \( x^{-2}y^3 \) (💎) as they are the same expression.

5. \( \frac{1}{x^3} \) (⭐) can be matched with \( x^{-3} \) (💎) since \( \frac{1}{x^3} = x^{-3} \).

6. \( 1 \) (⭐) remains unmatched as there is no specific partner among diamonds that is equivalent.

7. \( 3x^2 \) (⭐) can also remain unmatched as there is no specific partner among diamonds that is equivalent.

Therefore, the matches are:

1. \( 1/x \) ⭐ matches (x^{-1}) 💎
2. \( 3/x^4 \) ⭐ matches (3x^{-4}) 💎
3. \( y^3x^2 \) ⭐ matches (x^2y^3) 💎
4. \( x^{-2}y^3 \) ⭐ matches (x^{-2}y^3) 💎
5. \( 1/x^3 \) ⭐ matches (x^{-3}) 💎

Remaining unmatched cards are:

• \( 1 \) ⭐
• \( 3x^2 \) ⭐

You can now proceed with these matches as per the directions provided on the screen for the drag and drop action.