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Answer :
Sure! Let's go through each part of the question step-by-step:
1. Calculate [tex]\(-77 \times -79\)[/tex]:
- When you multiply two negative numbers, the result is positive.
- [tex]\(-77 \times -79 = 6083\)[/tex].
2. Calculate [tex]\(-18 \times 10\)[/tex]:
- When you multiply a negative number by a positive number, the result is negative.
- [tex]\(-18 \times 10 = -180\)[/tex].
3. Calculate [tex]\(-(-7)^2 + -7^2\)[/tex]:
- First, find [tex]\((-7)^2\)[/tex]: Squaring a negative number results in a positive number.
[tex]\((-7)^2 = 49\)[/tex].
- Then, calculate [tex]\(-(-7)^2\)[/tex] which is [tex]\(-49\)[/tex].
- Now for [tex]\(-7^2\)[/tex]: It's the same as squaring 7 and then making it negative.
[tex]\(-7^2 = -49\)[/tex].
- Add these results: [tex]\(-49 + -49 = -98\)[/tex].
4. Calculate [tex]\((-5)^2 + (-5)^3\)[/tex]:
- First, calculate [tex]\((-5)^2\)[/tex]: [tex]\((-5)^2 = 25\)[/tex] because squaring a negative number gives a positive result.
- Then, calculate [tex]\((-5)^3\)[/tex]: A negative number raised to an odd power remains negative.
[tex]\((-5)^3 = -125\)[/tex].
- Add these results: [tex]\(25 + (-125) = -100\)[/tex].
Now, arrange the list of integers in ascending order:
- The list is: [tex]\(100, -1000, 1000, 100, 10000, -10000\)[/tex].
- Ascending order means arranging from smallest to largest.
- The sorted list is: [tex]\([-10000, -1000, 100, 100, 1000, 10000]\)[/tex].
I hope this step-by-step walkthrough helps you understand the calculations! Let me know if you have any questions.
1. Calculate [tex]\(-77 \times -79\)[/tex]:
- When you multiply two negative numbers, the result is positive.
- [tex]\(-77 \times -79 = 6083\)[/tex].
2. Calculate [tex]\(-18 \times 10\)[/tex]:
- When you multiply a negative number by a positive number, the result is negative.
- [tex]\(-18 \times 10 = -180\)[/tex].
3. Calculate [tex]\(-(-7)^2 + -7^2\)[/tex]:
- First, find [tex]\((-7)^2\)[/tex]: Squaring a negative number results in a positive number.
[tex]\((-7)^2 = 49\)[/tex].
- Then, calculate [tex]\(-(-7)^2\)[/tex] which is [tex]\(-49\)[/tex].
- Now for [tex]\(-7^2\)[/tex]: It's the same as squaring 7 and then making it negative.
[tex]\(-7^2 = -49\)[/tex].
- Add these results: [tex]\(-49 + -49 = -98\)[/tex].
4. Calculate [tex]\((-5)^2 + (-5)^3\)[/tex]:
- First, calculate [tex]\((-5)^2\)[/tex]: [tex]\((-5)^2 = 25\)[/tex] because squaring a negative number gives a positive result.
- Then, calculate [tex]\((-5)^3\)[/tex]: A negative number raised to an odd power remains negative.
[tex]\((-5)^3 = -125\)[/tex].
- Add these results: [tex]\(25 + (-125) = -100\)[/tex].
Now, arrange the list of integers in ascending order:
- The list is: [tex]\(100, -1000, 1000, 100, 10000, -10000\)[/tex].
- Ascending order means arranging from smallest to largest.
- The sorted list is: [tex]\([-10000, -1000, 100, 100, 1000, 10000]\)[/tex].
I hope this step-by-step walkthrough helps you understand the calculations! Let me know if you have any questions.
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