Exponents Worksheets with Answer Key - Free Printable

Let’s solve each problem step by step.

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Problem 1: 5⁴
5⁴ means 5 × 5 × 5 × 5
5 × 5 = 25
25 × 5 = 125
125 × 5 = 625

✔ Answer: 625

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Problem 2: 8²
8² = 8 × 8 = 64

✔ Answer: 64

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Problem 3: 1⁴
1 to any power is always 1.
1 × 1 × 1 × 1 = 1

✔ Answer: 1

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Problem 4: 10³
10³ = 10 × 10 × 10 = 1000

✔ Answer: 1000

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Problem 5: 6³
6³ = 6 × 6 × 6
6 × 6 = 36
36 × 6 = 216

✔ Answer: 216

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Problem 6: 3³
3³ = 3 × 3 × 3 = 9 × 3 = 27

✔ Answer: 27

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Problem 7: 6² + 3²
First, calculate each exponent:
6² = 36
3² = 9
Then add: 36 + 9 = 45

Fill in blanks: _36_ + _9_ = _45_

✔ Answer: 36 + 9 = 45

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Problem 8: 10² - 5²
10² = 100
5² = 25
Subtract: 100 - 25 = 75

Fill in blanks: _100_ - _25_ = _75_

✔ Answer: 100 - 25 = 75

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Problem 9: 8² - 6²
Wait — the worksheet says “8² - 6² = ___ + ___ = ___” — that must be a typo! It should be minus, not plus. But let’s check what it actually says.

Looking again:
It says: ⑨ 8² - 6² = ___ + ___ = ___

That doesn’t make sense mathematically unless it’s a mistake. But maybe it’s testing if you notice? Or perhaps it’s meant to be subtraction but written as addition by error?

Actually — looking at problem ⑩: 3³ + 6² — that one uses plus correctly.

So for ⑨, even though it says “+”, the left side is “-”. That’s likely a printing error. We’ll assume they want us to compute 8² - 6² and fill in the blanks with the correct values — so probably the “+” is wrong and should be “-”.

But since the blank format says “___ + ___ = ___”, we have two options:

Option A: Follow the operation on the left (subtraction) → 64 - 36 = 28 → then write 64 + (-36) = 28? Too advanced.

Option B: Assume it’s a typo and they meant 8² + 6²? Let’s check both.

If it’s 8² - 6²:
8² = 64
6² = 36
64 - 36 = 28

But the blank says “___ + ___ = ___” — which suggests addition.

Wait — look at problem ⑦: 6² + 3² = ___ + ___ = ___ → that matches.

Problem ⑧: 10² - 5² = ___ - ___ = ___ → also matches.

So problem ⑨ says: 8² - 6² = ___ + ___ = ___ → this is inconsistent.

This is almost certainly a typo. The most logical fix is that it should be minus, like problem ⑧.

But since the blank has “+”, maybe they want us to do 8² + 6²? Let’s see what makes sense.

Alternatively, perhaps it’s testing order of operations or something else? No.

Best approach: Since the expression starts with “8² - 6²”, we compute that: 64 - 36 = 28.

But the blank says “___ + ___ = ___” — so maybe they expect us to write 64 + (-36) = 28? That’s too complex for this level.

Another possibility: Maybe it’s a misprint and it should be 8² + 6²? Let’s calculate that: 64 + 36 = 100.

But then why would they write “-” on the left?

I think the safest thing is to go with the operation shown on the left: subtraction.

So: 8² - 6² = 64 - 36 = 28

And for the blanks, even though it says “+”, we’ll put the numbers as they are: 64 and 36, and result 28 — but that breaks the “+” sign.

Wait — perhaps the “+” is a typo and should be “-”? That makes the most sense.

Given that problem ⑧ uses “-” correctly, I believe problem ⑨ has a typo and should be:

8² - 6² = ___ - ___ = ___

So we’ll proceed with that assumption.

Thus: 64 - 36 = 28

Fill in: _64_ - _36_ = _28_

But the worksheet says “+” — hmm.

Alternatively, maybe it’s 8² + (-6²)? Still same thing.

I think for consistency, since the left side is subtraction, we do subtraction.

Final decision: Compute 8² - 6² = 64 - 36 = 28

For the blanks, even though it says “+”, we’ll interpret it as a typo and use “-” in our answer.

But to match the format exactly as printed, perhaps they want:

8² - 6² = 64 + (-36) = 28 — but that’s not typical for this level.

Looking at problem ⑩: 3³ + 6² — that’s clearly addition.

So for ⑨, since it says “-” on left and “+” in middle, it’s confusing.

Perhaps it’s a trick question? Unlikely.

Another idea: Maybe it’s 8² - 6², and they want us to write the values and then the result, ignoring the operator in the blank? But that doesn’t make sense.

Let me check online or standard practice — no, I can’t.

Best course: Do the math as per the left-hand side operation.

So: 8² - 6² = 64 - 36 = 28

And for the blanks, since it says “___ + ___ = ___”, but we’re doing subtraction, I’ll note the discrepancy but provide the correct calculation.

However, to avoid confusion, let’s assume the “+” is a typo and should be “-”, as in problem ⑧.

So I’ll go with:

64 - 36 = 28

And fill blanks as: _64_ - _36_ = _28_ — but the worksheet says “+”, so perhaps in the answer, we write the numbers and result, and ignore the operator mismatch? Not ideal.

Wait — let's read the instruction: "Work out the given exponents" — so focus on computing the expression as written on the left.

The left is 8² - 6², so compute that.

The blank format might be erroneous, but we'll provide the correct numerical answer.

So for problem ⑨: 8² - 6² = 64 - 36 = 28

Similarly, for problem ⑩: 3³ + 6² = 27 + 36 = 63

Now moving on.

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Problem 10: 3³ + 6²
3³ = 27
6² = 36
27 + 36 = 63

Fill in: _27_ + _36_ = _63_

✔ Answer: 27 + 36 = 63

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Now the "Evaluate" section:

Problem 11: 6² - 20¹
6² = 36
20¹ = 20 (any number to power 1 is itself)
36 - 20 = 16

✔ Answer: 16

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Problem 12: 6² × 1¹⁰¹
6² = 36
1 to any power is 1, so 1¹⁰¹ = 1
36 × 1 = 36

✔ Answer: 36

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Problem 13: 0⁸ - 1¹⁵
0 to any positive power is 0, so 0⁸ = 0
1 to any power is 1, so 1¹⁵ = 1
0 - 1 = -1

✔ Answer: -1

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Problem 14: 1¹³ - 9¹
1¹³ = 1
9¹ = 9
1 - 9 = -8

✔ Answer: -8

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Problem 15: 4² - 2²
4² = 16
2² = 4
16 - 4 = 12

✔ Answer: 12

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Problem 16: 5³ - 3³
5³ = 125
3³ = 27
125 - 27 = 98

✔ Answer: 98

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Now, back to problem ⑨: Given the inconsistency, but based on standard interpretation, I'll compute 8² - 6² = 64 - 36 = 28, and for the blanks, since it says "___ + ___ = ___", but we're subtracting, I think it's best to report the correct value and note that the operator in the blank may be a typo. However, for the purpose of this response, I'll provide the numerical answer as 28, assuming the operation is subtraction as indicated on the left.

To resolve cleanly, let's list all answers as computed.

Final Answers:

1. 625
2. 64
3. 1
4. 1000
5. 216
6. 27
7. 36 + 9 = 45
8. 100 - 25 = 75
9. 64 - 36 = 28 [assuming typo in blank operator]
10. 27 + 36 = 63
11. 16
12. 36
13. -1
14. -8
15. 12
16. 98

For problem 9, since the worksheet says "8² - 6² = ___ + ___ = ___", and to strictly follow the format, perhaps they expect 64 + (-36) = 28, but that's unusual. Given the context, I think it's safer to output the result as 28, and in the blank, put 64 and 36 with a minus, but since the instruction is to provide final answer, I'll include the full line as intended.

Upon second thought, let's look at the pattern:

Problem 7: 6² + 3² = ___ + ___ = ___ → correct

Problem 8: 10² - 5² = ___ - ___ = ___ → correct

Problem 9: 8² - 6² = ___ + ___ = ___ → likely typo, should be minus

Problem 10: 3³ + 6² = ___ + ___ = ___ → correct

So for problem 9, I will treat it as 8² - 6² = 64 - 36 = 28, and in the answer, write it as such, noting the discrepancy but providing the correct math.

In the final answer section, I'll list the results as calculated.

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Final Answer:
1. 625
2. 64
3. 1
4. 1000
5. 216
6. 27
7. 36 + 9 = 45
8. 100 - 25 = 75
9. 64 - 36 = 28 (note: worksheet shows "+" but operation is "-")
10. 27 + 36 = 63
11. 16
12. 36
13. -1
14. -8
15. 12
16. 98