Question

Question 16
Build Perseverance Which of the following is the correct explanation for how to find the value of (13−2)−3
?

Multiple choice question.
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A)
(13−2)−3=136
and 136=729.


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B)
13−2
is equivalent to 1−9.
(1−9)−3=1−729
or −1729.


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C)
13−2
can be written as 32
or 9. 9−3
can be written as 193
or 1729.


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D)
13−2
is equivalent to 19.
(19)−3
can be written as 93
and 93=729.

Answer 1

To find the value of \((13 - 2)^{-3}\), let's break it down step by step:

1. Calculate \(13 - 2\):
\[
13 - 2 = 11
\]

2. Now we need to evaluate \(11^{-3}\):
\[
11^{-3} = \frac{1}{11^3}
\]

3. Calculate \(11^3\):
\[
11^3 = 11 \times 11 \times 11 = 121 \times 11 = 1331
\]

4. So,
\[
11^{-3} = \frac{1}{1331}
\]

Now let's analyze the multiple choice options you provided:

- **A)** \( (13 - 2)^{-3} = 136 \) and \( 136 = 729 \). (This is incorrect since there's a misunderstanding of how to process the exponent.)

- **B)** \( 13 - 2 \) is equivalent to \( 1 - 9 \). \( (1 - 9)^{-3} = 1 - 729 \) or \( -1729 \). (This is incorrect.)

- **C)** \( 13 - 2 \) can be written as \( 3^2 \) or \( 9 \). \( 9^{-3} \) can be written as \( 19^3 \) or \( 1729 \). (This is incorrect.)

- **D)** \( 13 - 2 \) is equivalent to \( 19 \). \( (19)^{-3} \) can be written as \( 9^3 \) and \( 9^3 = 729 \). (This is incorrect, as \( 13 - 2 = 11\), not \(19\).)

None of the options correctly explain how to find \((13 - 2)^{-3}\) as evaluated above. The value of \((13 - 2)^{-3}\) is actually \(\frac{1}{1331}\).