Printable primary math worksheet for math grades 1 to 6 based on ... - Free Printable

Let's solve each problem step by step. The task is to add and subtract exponents, but note: we are not combining exponents using exponent rules (like $ a^m \cdot a^n = a^{m+n} $), because these are evaluations of expressions involving powers, then performing arithmetic operations (addition or subtraction) on the results.

We will:

1. Evaluate each exponent.
2. Perform the addition or subtraction.

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Problem 1:

$ 10^2 - (-10^3) $

- $ 10^2 = 100 $
- $ 10^3 = 1000 $, so $ -10^3 = -1000 $
- But note: the expression is $ -(-10^3) $? Wait — let's be careful.

Actually:
$ -(-10^3) $ → This is ambiguous in notation. But standard order of operations says exponentiation comes before negation unless parentheses specify otherwise.

But here:
It's written as: $ 10^2 - (-10^3) $

So:
- $ 10^2 = 100 $
- $ -10^3 = -(10^3) = -1000 $
- So $ -(-10^3) = -(-1000) = +1000 $

Wait! The expression is:
$ 10^2 - (-10^3) $

That means:
= $ 100 - (-1000) = 100 + 1000 = 1100 $

✔ Answer: 1100

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Problem 2:

$ 2^3 + 2^4 $

- $ 2^3 = 8 $
- $ 2^4 = 16 $
- $ 8 + 16 = 24 $

✔ Answer: 24

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Problem 3:

$ 8^1 - 10^2 $

- $ 8^1 = 8 $
- $ 10^2 = 100 $
- $ 8 - 100 = -92 $

✔ Answer: -92

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Problem 4:

$ 11^2 + (-5^3) $

- $ 11^2 = 121 $
- $ 5^3 = 125 $, so $ -5^3 = -125 $
- $ 121 + (-125) = -4 $

✔ Answer: -4

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Problem 5:

$ 12^2 + 20^2 $

- $ 12^2 = 144 $
- $ 20^2 = 400 $
- $ 144 + 400 = 544 $

✔ Answer: 544

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Problem 6:

$ 15^3 - 15^2 $

- $ 15^3 = 15 \times 15 \times 15 = 225 \times 15 = 3375 $
- $ 15^2 = 225 $
- $ 3375 - 225 = 3150 $

✔ Answer: 3150

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Problem 7:

$ 5^3 - 10^3 $

- $ 5^3 = 125 $
- $ 10^3 = 1000 $
- $ 125 - 1000 = -875 $

✔ Answer: -875

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Problem 8:

$ 10^2 - (-9^3) $

- $ 10^2 = 100 $
- $ 9^3 = 729 $, so $ -9^3 = -729 $
- Then $ -(-9^3) = -(-729) = +729 $? No!

Wait: expression is $ 10^2 - (-9^3) $

So:
- $ -9^3 = -(9^3) = -729 $
- So $ 10^2 - (-729) = 100 + 729 = 829 $

✔ Answer: 829

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Problem 9:

$ 8^4 - (-10^3) $

- $ 8^4 = 8 \times 8 \times 8 \times 8 = 64 \times 64 = 4096 $
- $ 10^3 = 1000 $, so $ -10^3 = -1000 $
- $ 8^4 - (-10^3) = 4096 - (-1000) = 4096 + 1000 = 5096 $

✔ Answer: 5096

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Problem 10:

$ 11^3 - 14^3 $

- $ 11^3 = 11 \times 11 \times 11 = 121 \times 11 = 1331 $
- $ 14^3 = 14 \times 14 \times 14 = 196 \times 14 = 2744 $
- $ 1331 - 2744 = -1413 $

✔ Answer: -1413

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Problem 11:

$ 12^2 + 13^3 $

- $ 12^2 = 144 $
- $ 13^3 = 13 \times 13 \times 13 = 169 \times 13 = 2197 $
- $ 144 + 2197 = 2341 $

✔ Answer: 2341

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Problem 12:

$ 10^4 + 10^3 $

- $ 10^4 = 10000 $
- $ 10^3 = 1000 $
- $ 10000 + 1000 = 11000 $

✔ Answer: 11000

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Problem 13:

$ 25^2 + (-3^3) $

- $ 25^2 = 625 $
- $ 3^3 = 27 $, so $ -3^3 = -27 $
- $ 625 + (-27) = 598 $

✔ Answer: 598

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Problem 14:

$ 20^1 + 20^0 $

- $ 20^1 = 20 $
- $ 20^0 = 1 $ (any non-zero number to power 0 is 1)
- $ 20 + 1 = 21 $

✔ Answer: 21

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Problem 15:

$ 15^3 - 14^3 $

- $ 15^3 = 3375 $ (from earlier)
- $ 14^3 = 2744 $ (from earlier)
- $ 3375 - 2744 = 631 $

✔ Answer: 631

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Problem 16:

$ 11^2 - (-11^3) $

- $ 11^2 = 121 $
- $ 11^3 = 1331 $, so $ -11^3 = -1331 $
- $ 11^2 - (-11^3) = 121 - (-1331) = 121 + 1331 = 1452 $

✔ Answer: 1452

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Problem 17:

$ 3^3 - (-30^2) $

- $ 3^3 = 27 $
- $ 30^2 = 900 $, so $ -30^2 = -900 $
- $ 3^3 - (-30^2) = 27 - (-900) = 27 + 900 = 927 $

✔ Answer: 927

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Problem 18:

$ 10^0 + 10^3 $

- $ 10^0 = 1 $
- $ 10^3 = 1000 $
- $ 1 + 1000 = 1001 $

✔ Answer: 1001

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✔ Final Answers:

| Expression | Answer |
|----------|--------|
| $ 10^2 - (-10^3) $ | 1100 |
| $ 2^3 + 2^4 $ | 24 |
| $ 8^1 - 10^2 $ | -92 |
| $ 11^2 + (-5^3) $ | -4 |
| $ 12^2 + 20^2 $ | 544 |
| $ 15^3 - 15^2 $ | 3150 |
| $ 5^3 - 10^3 $ | -875 |
| $ 10^2 - (-9^3) $ | 829 |
| $ 8^4 - (-10^3) $ | 5096 |
| $ 11^3 - 14^3 $ | -1413 |
| $ 12^2 + 13^3 $ | 2341 |
| $ 10^4 + 10^3 $ | 11000 |
| $ 25^2 + (-3^3) $ | 598 |
| $ 20^1 + 20^0 $ | 21 |
| $ 15^3 - 14^3 $ | 631 |
| $ 11^2 - (-11^3) $ | 1452 |
| $ 3^3 - (-30^2) $ | 927 |
| $ 10^0 + 10^3 $ | 1001 |

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📌 Key Notes:

- Always evaluate exponents first.
- Pay attention to order of operations: negative signs apply after exponentiation unless parentheses indicate otherwise.
- For example: $ -10^3 = -(10^3) = -1000 $, not $ (-10)^3 = -1000 $ — same result here, but different in other cases!
- But $ (-10)^3 = -1000 $, while $ -10^3 = -1000 $ — coincidentally same, but if it were even exponent: $ (-10)^2 = 100 $, $ -10^2 = -100 $

So always be cautious with placement of parentheses.

Let me know if you'd like this formatted as a printable answer sheet!