MathsAges 13-15

Laws of indices (exponents)

Apply the multiplication, division and power laws of indices to simplify algebraic powers. Review suitability for your learners before teaching.

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Age band:Ages 13-15 Ages 16-18

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Worksheet StudioPractice pack · Ages 13-15

Laws of indices (exponents)

Take your time. Show your thinking.

1. Simplify x^10 ÷ x^6 in the form x^n.
10 · 6 · Laws of indices (exponents)
2. Simplify x^19 ÷ x^10 in the form x^n.
19 · 10 · Laws of indices (exponents)
3. Simplify x^8 × x^7 in the form x^n.
8 · 7 · Laws of indices (exponents)
4. Simplify x^10 × x^12 in the form x^n.
10 · 12 · Laws of indices (exponents)
5. Simplify x^2 × x^5 in the form x^n.
2 · 5 · Laws of indices (exponents)
6. Simplify x^6 × x^5 in the form x^n.
6 · 5 · Laws of indices (exponents)
7. Simplify x^6 × x^4 in the form x^n.
6 · 4 · Laws of indices (exponents)
8. Simplify x^8 ÷ x^3 in the form x^n.
8 · 3 · Laws of indices (exponents)
9. Simplify x^16 ÷ x^10 in the form x^n.
16 · 10 · Laws of indices (exponents)
10. Simplify x^12 ÷ x^9 in the form x^n.
12 · 9 · Laws of indices (exponents)
11. Simplify x^5 ÷ x^4 in the form x^n.
5 · 4 · Laws of indices (exponents)
12. Simplify x^12 × x^3 in the form x^n.
12 · 3 · Laws of indices (exponents)

12 questions · Seed 45 · Age guidance, not curriculum certification

View the answer key

Worksheet StudioAnswer key · Ages 13-15

Laws of indices (exponents)

Answers and reasoning. Review before teaching.

1. Simplify x^10 ÷ x^6 in the form x^n.
x^4
When dividing powers with the same base, subtract the exponents: 10 − 6 = 4, giving x^4.
2. Simplify x^19 ÷ x^10 in the form x^n.
x^9
When dividing powers with the same base, subtract the exponents: 19 − 10 = 9, giving x^9.
3. Simplify x^8 × x^7 in the form x^n.
x^15
When multiplying powers with the same base, add the exponents: 8 + 7 = 15, giving x^15.
4. Simplify x^10 × x^12 in the form x^n.
x^22
When multiplying powers with the same base, add the exponents: 10 + 12 = 22, giving x^22.
5. Simplify x^2 × x^5 in the form x^n.
x^7
When multiplying powers with the same base, add the exponents: 2 + 5 = 7, giving x^7.
6. Simplify x^6 × x^5 in the form x^n.
x^11
When multiplying powers with the same base, add the exponents: 6 + 5 = 11, giving x^11.
7. Simplify x^6 × x^4 in the form x^n.
x^10
When multiplying powers with the same base, add the exponents: 6 + 4 = 10, giving x^10.
8. Simplify x^8 ÷ x^3 in the form x^n.
x^5
When dividing powers with the same base, subtract the exponents: 8 − 3 = 5, giving x^5.
9. Simplify x^16 ÷ x^10 in the form x^n.
x^6
When dividing powers with the same base, subtract the exponents: 16 − 10 = 6, giving x^6.
10. Simplify x^12 ÷ x^9 in the form x^n.
x^3
When dividing powers with the same base, subtract the exponents: 12 − 9 = 3, giving x^3.
11. Simplify x^5 ÷ x^4 in the form x^n.
x^1
When dividing powers with the same base, subtract the exponents: 5 − 4 = 1, giving x^1.
12. Simplify x^12 × x^3 in the form x^n.
x^15
When multiplying powers with the same base, add the exponents: 12 + 3 = 15, giving x^15.

12 questions · Seed 45 · Age guidance, not curriculum certification

Worksheet StudioPractice pack · Ages 13-15

Laws of indices (exponents)

Take your time. Show your thinking.

1. Simplify x^10 ÷ x^6 in the form x^n.
10 · 6 · Laws of indices (exponents)
2. Simplify x^19 ÷ x^10 in the form x^n.
19 · 10 · Laws of indices (exponents)
3. Simplify x^8 × x^7 in the form x^n.
8 · 7 · Laws of indices (exponents)
4. Simplify x^10 × x^12 in the form x^n.
10 · 12 · Laws of indices (exponents)
5. Simplify x^2 × x^5 in the form x^n.
2 · 5 · Laws of indices (exponents)
6. Simplify x^6 × x^5 in the form x^n.
6 · 5 · Laws of indices (exponents)
7. Simplify x^6 × x^4 in the form x^n.
6 · 4 · Laws of indices (exponents)
8. Simplify x^8 ÷ x^3 in the form x^n.
8 · 3 · Laws of indices (exponents)
9. Simplify x^16 ÷ x^10 in the form x^n.
16 · 10 · Laws of indices (exponents)
10. Simplify x^12 ÷ x^9 in the form x^n.
12 · 9 · Laws of indices (exponents)
11. Simplify x^5 ÷ x^4 in the form x^n.
5 · 4 · Laws of indices (exponents)
12. Simplify x^12 × x^3 in the form x^n.
12 · 3 · Laws of indices (exponents)

12 questions · Seed 45 · Age guidance, not curriculum certification

Worksheet StudioAnswer key · Ages 13-15

Laws of indices (exponents)

Answers and reasoning. Review before teaching.

1. Simplify x^10 ÷ x^6 in the form x^n.
x^4
When dividing powers with the same base, subtract the exponents: 10 − 6 = 4, giving x^4.
2. Simplify x^19 ÷ x^10 in the form x^n.
x^9
When dividing powers with the same base, subtract the exponents: 19 − 10 = 9, giving x^9.
3. Simplify x^8 × x^7 in the form x^n.
x^15
When multiplying powers with the same base, add the exponents: 8 + 7 = 15, giving x^15.
4. Simplify x^10 × x^12 in the form x^n.
x^22
When multiplying powers with the same base, add the exponents: 10 + 12 = 22, giving x^22.
5. Simplify x^2 × x^5 in the form x^n.
x^7
When multiplying powers with the same base, add the exponents: 2 + 5 = 7, giving x^7.
6. Simplify x^6 × x^5 in the form x^n.
x^11
When multiplying powers with the same base, add the exponents: 6 + 5 = 11, giving x^11.
7. Simplify x^6 × x^4 in the form x^n.
x^10
When multiplying powers with the same base, add the exponents: 6 + 4 = 10, giving x^10.
8. Simplify x^8 ÷ x^3 in the form x^n.
x^5
When dividing powers with the same base, subtract the exponents: 8 − 3 = 5, giving x^5.
9. Simplify x^16 ÷ x^10 in the form x^n.
x^6
When dividing powers with the same base, subtract the exponents: 16 − 10 = 6, giving x^6.
10. Simplify x^12 ÷ x^9 in the form x^n.
x^3
When dividing powers with the same base, subtract the exponents: 12 − 9 = 3, giving x^3.
11. Simplify x^5 ÷ x^4 in the form x^n.
x^1
When dividing powers with the same base, subtract the exponents: 5 − 4 = 1, giving x^1.
12. Simplify x^12 × x^3 in the form x^n.
x^15
When multiplying powers with the same base, add the exponents: 12 + 3 = 15, giving x^15.

12 questions · Seed 45 · Age guidance, not curriculum certification