Exponents Practice Worksheet for math students to work out and evaluate various exponential expressions.
Exponents Practice Worksheet with problems involving exponentiation, evaluation, and arithmetic operations with exponents.
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Step-by-step solution for: Exponents Worksheets with Answer Key
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Show Answer Key & Explanations
Step-by-step solution for: Exponents Worksheets with Answer Key
Let’s solve each problem step by step.
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Section 1: Work out the given exponents
[1] 5⁴ = 5 × 5 × 5 × 5
= 25 × 5 × 5
= 125 × 5
= 625
[2] 8² = 8 × 8 = 64
[3] 1⁴ = 1 × 1 × 1 × 1 = 1
[4] 10³ = 10 × 10 × 10 = 1000
[5] 6³ = 6 × 6 × 6
= 36 × 6
= 216
[6] 3³ = 3 × 3 × 3
= 9 × 3
= 27
[7] 6² + 3² = (6×6) + (3×3) = 36 + 9 = 45
So: 36 + 9 = 45
[8] 10² - 5² = (10×10) - (5×5) = 100 - 25 = 75
So: 100 - 25 = 75
[9] 8² - 6² = (8×8) - (6×6) = 64 - 36 = 28
Wait — the worksheet says “___ + ___ = ___” but it’s subtraction. That might be a typo. But since it says “+”, let’s check: maybe they want us to write it as addition of negative? No, that doesn’t make sense for this level. Probably a mistake in the worksheet. We’ll go with correct math: 64 - 36 = 28. But if forced to fill blanks as written: 64 + (-36) = 28? Not likely. Let’s assume it’s a typo and should be minus. But the blank format says “__ + __ = __”. Hmm. Maybe they meant to write 8² + (-6²)? Still odd. Alternatively, perhaps it’s misprinted and should be 8² + 6²? But no, the operation is clearly minus. I think we should just compute correctly: 64 - 36 = 28. For the blanks, maybe they expect: 64 - 36 = 28, but since it says “+”, perhaps ignore and do correct math. Wait — looking again at [9]: “8² - 6² = __ + __ = __” — that must be an error. Same with [10]. Let’s look at [10]: “3³ + 6² = __ + __ = __” — that one makes sense. So probably [9] has a typo and should be “-” not “+”. Since we’re solving accurately, we’ll do:
For [9]: 8² - 6² = 64 - 36 = 28 → so if blanks are for intermediate steps: 64 - 36 = 28. But since it says “+”, maybe skip or note. To follow instructions, let’s assume it’s a typo and proceed with correct calculation. Perhaps the “+” is a mistake and should be “-”. We’ll write: 64 - 36 = 28. But to fit the blank format as printed, maybe they want: 64 + (-36) = 28? Unlikely for this level. Better to correct silently. I’ll put: 64 - 36 = 28, and for blanks: first blank 64, second blank 36, third 28 — even though operator is wrong. Or perhaps the worksheet meant to have two separate operations? No. Let’s move on and handle [10] which is clear.
Actually, re-examining: [9] says “8² - 6² = __ + __ = __” — this is inconsistent. Likely a printing error. In educational context, we teach correct math. So I will calculate 8² - 6² = 64 - 36 = 28. For the blanks, since it says “+”, but mathematically it’s minus, I’ll still fill the numbers: 64 and 36, then result 28, noting the operator is wrong. But to avoid confusion, perhaps the intended was to show expansion: like 64 - 36, but written as sum? No. Another idea: maybe they want us to write it as 64 + (-36)? But that’s advanced. I think best to do correct math and fill blanks as 64, 36, 28 — assuming the “+” is a typo and should be “-”.
Similarly, [10] is fine: 3³ + 6² = 27 + 36 = 63
So:
[9] 8² - 6² = 64 - 36 = 28 → blanks: 64, 36, 28 (ignoring the "+" as typo)
[10] 3³ + 6² = 27 + 36 = 63
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Section 2: Evaluate
[11] 6² - 20¹ = 36 - 20 = 16
[12] 6² × 1¹⁰¹ = 36 × 1 = 36 (since any power of 1 is 1)
[13] 0⁸ - 1¹⁵ = 0 - 1 = -1 (0 to any positive power is 0; 1 to any power is 1)
[14] 1¹³ - 9¹ = 1 - 9 = -8
[15] 4² - 2² = 16 - 4 = 12
[16] 5³ - 3³ = 125 - 27 = 98
---
Now, compiling all answers:
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 should be "-")*
[10] 27 + 36 = 63
[11] 16
[12] 36
[13] -1
[14] -8
[15] 12
[16] 98
---
Section 1: Work out the given exponents
[1] 5⁴ = 5 × 5 × 5 × 5
= 25 × 5 × 5
= 125 × 5
= 625
[2] 8² = 8 × 8 = 64
[3] 1⁴ = 1 × 1 × 1 × 1 = 1
[4] 10³ = 10 × 10 × 10 = 1000
[5] 6³ = 6 × 6 × 6
= 36 × 6
= 216
[6] 3³ = 3 × 3 × 3
= 9 × 3
= 27
[7] 6² + 3² = (6×6) + (3×3) = 36 + 9 = 45
So: 36 + 9 = 45
[8] 10² - 5² = (10×10) - (5×5) = 100 - 25 = 75
So: 100 - 25 = 75
[9] 8² - 6² = (8×8) - (6×6) = 64 - 36 = 28
Wait — the worksheet says “___ + ___ = ___” but it’s subtraction. That might be a typo. But since it says “+”, let’s check: maybe they want us to write it as addition of negative? No, that doesn’t make sense for this level. Probably a mistake in the worksheet. We’ll go with correct math: 64 - 36 = 28. But if forced to fill blanks as written: 64 + (-36) = 28? Not likely. Let’s assume it’s a typo and should be minus. But the blank format says “__ + __ = __”. Hmm. Maybe they meant to write 8² + (-6²)? Still odd. Alternatively, perhaps it’s misprinted and should be 8² + 6²? But no, the operation is clearly minus. I think we should just compute correctly: 64 - 36 = 28. For the blanks, maybe they expect: 64 - 36 = 28, but since it says “+”, perhaps ignore and do correct math. Wait — looking again at [9]: “8² - 6² = __ + __ = __” — that must be an error. Same with [10]. Let’s look at [10]: “3³ + 6² = __ + __ = __” — that one makes sense. So probably [9] has a typo and should be “-” not “+”. Since we’re solving accurately, we’ll do:
For [9]: 8² - 6² = 64 - 36 = 28 → so if blanks are for intermediate steps: 64 - 36 = 28. But since it says “+”, maybe skip or note. To follow instructions, let’s assume it’s a typo and proceed with correct calculation. Perhaps the “+” is a mistake and should be “-”. We’ll write: 64 - 36 = 28. But to fit the blank format as printed, maybe they want: 64 + (-36) = 28? Unlikely for this level. Better to correct silently. I’ll put: 64 - 36 = 28, and for blanks: first blank 64, second blank 36, third 28 — even though operator is wrong. Or perhaps the worksheet meant to have two separate operations? No. Let’s move on and handle [10] which is clear.
Actually, re-examining: [9] says “8² - 6² = __ + __ = __” — this is inconsistent. Likely a printing error. In educational context, we teach correct math. So I will calculate 8² - 6² = 64 - 36 = 28. For the blanks, since it says “+”, but mathematically it’s minus, I’ll still fill the numbers: 64 and 36, then result 28, noting the operator is wrong. But to avoid confusion, perhaps the intended was to show expansion: like 64 - 36, but written as sum? No. Another idea: maybe they want us to write it as 64 + (-36)? But that’s advanced. I think best to do correct math and fill blanks as 64, 36, 28 — assuming the “+” is a typo and should be “-”.
Similarly, [10] is fine: 3³ + 6² = 27 + 36 = 63
So:
[9] 8² - 6² = 64 - 36 = 28 → blanks: 64, 36, 28 (ignoring the "+" as typo)
[10] 3³ + 6² = 27 + 36 = 63
---
Section 2: Evaluate
[11] 6² - 20¹ = 36 - 20 = 16
[12] 6² × 1¹⁰¹ = 36 × 1 = 36 (since any power of 1 is 1)
[13] 0⁸ - 1¹⁵ = 0 - 1 = -1 (0 to any positive power is 0; 1 to any power is 1)
[14] 1¹³ - 9¹ = 1 - 9 = -8
[15] 4² - 2² = 16 - 4 = 12
[16] 5³ - 3³ = 125 - 27 = 98
---
Now, compiling all answers:
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 should be "-")*
[10] 27 + 36 = 63
[11] 16
[12] 36
[13] -1
[14] -8
[15] 12
[16] 98
Parent Tip: Review the logic above to help your child master the concept of math exponents worksheet.
