The image contains a list of mathematical expressions involving exponents and scientific notation. The task appears to be to simplify or evaluate each expression.
Let’s go through each one step by step:
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1. 2⁴ × 2² × 2⁶
When multiplying powers with the same base, add the exponents:
2⁴⁺²⁺⁶ = 2¹²
2¹² = 4096
✔ Correct answer:
4096
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2. 5³ × 5⁴ × 5²
Again, same base → add exponents:
5³⁺⁴⁺² = 5⁹
5⁹ = 1,953,125
✔ Correct answer:
1,953,125
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3. 3⁵ × 3⁷ × 3⁻⁹
Add exponents: 5 + 7 - 9 = 3
So, 3³ = 27
✔ Correct answer:
27
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4. 4⁶ × 4⁻² × 4⁻¹
Add exponents: 6 - 2 - 1 = 3
4³ = 64
✔ Correct answer:
64
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5. 7⁴ × 7⁻³ × 7²
Add exponents: 4 - 3 + 2 = 3
7³ = 343
✔ Correct answer:
343
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6. 10⁵ × 10⁻⁴ × 10³
Add exponents: 5 - 4 + 3 = 4
10⁴ = 10,000
✔ Correct answer:
10,000
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7. (2 × 10³) × (3 × 10⁴)
Multiply coefficients: 2 × 3 = 6
Multiply powers of 10: 10³ × 10⁴ = 10⁷
So, 6 × 10⁷ = 60,000,000
✔ Correct answer:
60,000,000
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8. (5 × 10²) × (4 × 10⁻¹)
Coefficients: 5 × 4 = 20
Powers of 10: 10² × 10⁻¹ = 10¹
So, 20 × 10¹ = 200
✔ Correct answer:
200
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9. (6 × 10⁵) × (2 × 10⁻³)
Coefficients: 6 × 2 = 12
Powers of 10: 10⁵ × 10⁻³ = 10²
So, 12 × 10² = 1,200
✔ Correct answer:
1,200
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10. (8 × 10⁴) × (5 × 10⁻²)
Coefficients: 8 × 5 = 40
Powers of 10: 10⁴ × 10⁻² = 10²
So, 40 × 10² = 4,000
✔ Correct answer:
4,000
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All answers have been verified.
Final Answer:
4096, 1953125, 27, 64, 343, 10000, 60000000, 200, 1200, 4000
Parent Tip: Review the logic above to help your child master the concept of math handbook transparency worksheet.
