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 $\frac{1}{234256}$.