#1. Formula Chart Matching

Question

Cards with the ⭐ are the rules from the formula chart. Match each term with its corresponding rule.
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.
5^−3

x^5·x^8

Product of Powers ⭐




am/an =a^m+n

Power of a Power ⭐

Negative Exponent⭐


a^−n = 1/a^n​

b^5/b^10​

Quotient of Powers ⭐




a^m/a^n​ = a^(m−n)

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

To detach, drag the BOTTOM card away.

(2a^4)^3

Answer 1

Here's how the terms match up with the corresponding rules from the formula chart:

1. 5^−3

   • Rule: Negative Exponent ⭐
   • Match: \( a^{-n} = \frac{1}{a^n} \)

2. x^5·x^8

   • Rule: Product of Powers ⭐
   • Match: \( a^m \cdot a^n = a^{m+n} \)

3. (2a^4)^3

   • Rule: Power of a Power ⭐
   • Match: \( (a^m)^n = a^{m \cdot n} \)

4. b^5/b^10

   • Rule: Quotient of Powers ⭐
   • Match: \( \frac{a^m}{a^n} = a^{m-n} \)

5. am/an = a^(m−n)

   • Rule: Quotient of Powers ⭐
   • Match: \( \frac{a^m}{a^n} = a^{m-n} \)

Each term corresponds to a specific rule, and using the properties of exponents helps simplify and manipulate these expressions.