Connor and Helen are playing a matching game to practice working with the laws of exponents. Connor's card has 18

Question

.

Helen has 3 cards to choose from. One card has 2−3
. Another card has (12)−2
. The final card has (22)−4
.

Complete the statements below for each of Helen's cards.

Card 2−3
is the
Choose...
card. The rule for negative exponents is to
Choose...
which results in an answer of
Choose...
.
Question 2
Card (12)−2
is the
Choose...
card. The rule for negative exponents is to
Choose...
which results in an answer of
Choose...
.
Question 3
Card (22)−4
is the
Choose...
card. The rule for raising an exponent to an exponent is to
Choose...
which results in an answer of
Choose...
.

Answer 1

Let's go through each of Helen's cards one by one.

Card 1: \( 2^{-3} \)

• Card \( 2^{-3} \) is the exponent card.
• The rule for negative exponents is to take the reciprocal and change the sign of the exponent.
• This results in an answer of \( \frac{1}{2^3} = \frac{1}{8} \).

Card 2: \( (12)^{-2} \)

• Card \( (12)^{-2} \) is the exponent card.
• The rule for negative exponents is to take the reciprocal and change the sign of the exponent.
• This results in an answer of \( \frac{1}{12^2} = \frac{1}{144} \).

Card 3: \( (22)^{-4} \)

• Card \( (22)^{-4} \) is the exponent card.
• The rule for raising an exponent to an exponent is to multiply the exponents.
• This results in an answer of \( \frac{1}{22^4} = \frac{1}{234256} \).

Here’s the completed information for all three cards:

1. Card \( 2^{-3} \) is the exponent card. The rule for negative exponents is to take the reciprocal and change the sign of the exponent, which results in an answer of \(\frac{1}{8}\).

2. Card \( (12)^{-2} \) is the exponent card. The rule for negative exponents is to take the reciprocal and change the sign of the exponent, which results in an answer of \(\frac{1}{144}\).

3. Card \( (22)^{-4} \) is the exponent card. The rule for raising an exponent to an exponent is to multiply the exponents, which results in an answer of \(\frac{1}{234256}\).