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Power Rule of Exponents — Easy Worksheet 2
Grade 8 · MathSheets Name: ____________________ Date: __________
Simplify. Raise a power to a power by multiplying the exponents.
How to solve
To raise a power to a power, keep the base and multiply the exponents: (x3)4 = x12, because it is x3 · x3 · x3 · x3. When a whole monomial is raised to a power, raise every factor: (2x3 y)4 = 24 · x12 · y4 = 16x12 y4. A negative number to an odd power stays negative: (-2)3 = -8.
Example
(93)4 = 9
Answer: 12
Not quite. The answer is
💡 A power is raised to a power, so keep the base x and multiply the exponents: 7 × 5 = 35. So (x7)5 = x35, and the missing exponent is 35.
✓ Correct!
Not quite. The answer is
💡 A power is raised to a power, so keep the base x and multiply the exponents: 7 × 5 = 35. So (x7)5 = x35, and the missing exponent is 35.
💡 How to solve: Power Rule of Exponents
To raise a power to a power, keep the base and multiply the exponents: (x3)4 = x12, because it is x3 · x3 · x3 · x3. When a whole monomial is raised to a power, raise every factor: (2x3 y)4 = 24 · x12 · y4 = 16x12 y4. A negative number to an odd power stays negative: (-2)3 = -8.
Try a similar one
(n4)2 = n
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 A power is raised to a power, so keep the base a and multiply the exponents: 9 × 4 = 36. So (a9)4 = a36, and the missing exponent is 36.
✓ Correct!
Not quite. The answer is
💡 A power is raised to a power, so keep the base a and multiply the exponents: 9 × 4 = 36. So (a9)4 = a36, and the missing exponent is 36.
💡 How to solve: Power Rule of Exponents
To raise a power to a power, keep the base and multiply the exponents: (x3)4 = x12, because it is x3 · x3 · x3 · x3. When a whole monomial is raised to a power, raise every factor: (2x3 y)4 = 24 · x12 · y4 = 16x12 y4. A negative number to an odd power stays negative: (-2)3 = -8.
Try a similar one
(n3)5 = n
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 A power is raised to a power, so keep the base a and multiply the exponents: 7 × 5 = 35. So (a7)5 = a35, and the missing exponent is 35.
✓ Correct!
Not quite. The answer is
💡 A power is raised to a power, so keep the base a and multiply the exponents: 7 × 5 = 35. So (a7)5 = a35, and the missing exponent is 35.
💡 How to solve: Power Rule of Exponents
To raise a power to a power, keep the base and multiply the exponents: (x3)4 = x12, because it is x3 · x3 · x3 · x3. When a whole monomial is raised to a power, raise every factor: (2x3 y)4 = 24 · x12 · y4 = 16x12 y4. A negative number to an odd power stays negative: (-2)3 = -8.
Try a similar one
(a5)5 = a
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 A power is raised to a power, so keep the base b and multiply the exponents: 5 × 3 = 15. So (b5)3 = b15, and the missing exponent is 15.
✓ Correct!
Not quite. The answer is
💡 A power is raised to a power, so keep the base b and multiply the exponents: 5 × 3 = 15. So (b5)3 = b15, and the missing exponent is 15.
💡 How to solve: Power Rule of Exponents
To raise a power to a power, keep the base and multiply the exponents: (x3)4 = x12, because it is x3 · x3 · x3 · x3. When a whole monomial is raised to a power, raise every factor: (2x3 y)4 = 24 · x12 · y4 = 16x12 y4. A negative number to an odd power stays negative: (-2)3 = -8.
Try a similar one
(a5)4 = a
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 A power is raised to a power, so keep the base a and multiply the exponents: 8 × 4 = 32. So (a8)4 = a32, and the missing exponent is 32.
✓ Correct!
Not quite. The answer is
💡 A power is raised to a power, so keep the base a and multiply the exponents: 8 × 4 = 32. So (a8)4 = a32, and the missing exponent is 32.
💡 How to solve: Power Rule of Exponents
To raise a power to a power, keep the base and multiply the exponents: (x3)4 = x12, because it is x3 · x3 · x3 · x3. When a whole monomial is raised to a power, raise every factor: (2x3 y)4 = 24 · x12 · y4 = 16x12 y4. A negative number to an odd power stays negative: (-2)3 = -8.
Try a similar one
(b3)5 = b
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 A power is raised to a power, so keep the base b and multiply the exponents: 8 × 5 = 40. So (b8)5 = b40, and the missing exponent is 40.
✓ Correct!
Not quite. The answer is
💡 A power is raised to a power, so keep the base b and multiply the exponents: 8 × 5 = 40. So (b8)5 = b40, and the missing exponent is 40.
💡 How to solve: Power Rule of Exponents
To raise a power to a power, keep the base and multiply the exponents: (x3)4 = x12, because it is x3 · x3 · x3 · x3. When a whole monomial is raised to a power, raise every factor: (2x3 y)4 = 24 · x12 · y4 = 16x12 y4. A negative number to an odd power stays negative: (-2)3 = -8.
Try a similar one
(x5)3 = x
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 A power is raised to a power, so keep the base n and multiply the exponents: 9 × 2 = 18. So (n9)2 = n18, and the missing exponent is 18.
✓ Correct!
Not quite. The answer is
💡 A power is raised to a power, so keep the base n and multiply the exponents: 9 × 2 = 18. So (n9)2 = n18, and the missing exponent is 18.
💡 How to solve: Power Rule of Exponents
To raise a power to a power, keep the base and multiply the exponents: (x3)4 = x12, because it is x3 · x3 · x3 · x3. When a whole monomial is raised to a power, raise every factor: (2x3 y)4 = 24 · x12 · y4 = 16x12 y4. A negative number to an odd power stays negative: (-2)3 = -8.
Try a similar one
(a6)3 = a
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 A power is raised to a power, so keep the base x and multiply the exponents: 3 × 5 = 15. So (x3)5 = x15, and the missing exponent is 15.
✓ Correct!
Not quite. The answer is
💡 A power is raised to a power, so keep the base x and multiply the exponents: 3 × 5 = 15. So (x3)5 = x15, and the missing exponent is 15.
💡 How to solve: Power Rule of Exponents
To raise a power to a power, keep the base and multiply the exponents: (x3)4 = x12, because it is x3 · x3 · x3 · x3. When a whole monomial is raised to a power, raise every factor: (2x3 y)4 = 24 · x12 · y4 = 16x12 y4. A negative number to an odd power stays negative: (-2)3 = -8.
Try a similar one
(m8)5 = m
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
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Power Rule of Exponents — Easy Worksheet 2
Simplify. Raise a power to a power by multiplying the exponents.