Math Problem Statement

Solve the following exponents: 10^1, 1^8, 7^4, 10^9, 2^6, 7^1, 10^3, 10^8, 0^4, 7^6, 9^6, 3^1.

Solution

Let's go through the exponent problems in the image and solve them:

  1. 101=1010^1 = 10
  2. 18=11^8 = 1
  3. 74=7×7×7×7=24017^4 = 7 \times 7 \times 7 \times 7 = 2401
  4. 109=1,000,000,00010^9 = 1,000,000,000 (one billion)
  5. 26=2×2×2×2×2×2=642^6 = 2 \times 2 \times 2 \times 2 \times 2 \times 2 = 64
  6. 71=77^1 = 7
  7. 103=1,00010^3 = 1,000 (one thousand)
  8. 108=100,000,00010^8 = 100,000,000 (one hundred million)
  9. 04=00^4 = 0
  10. 76=7×7×7×7×7×7=1176497^6 = 7 \times 7 \times 7 \times 7 \times 7 \times 7 = 117649
  11. 96=9×9×9×9×9×9=531,4419^6 = 9 \times 9 \times 9 \times 9 \times 9 \times 9 = 531,441
  12. 31=33^1 = 3

Would you like any further explanations on how these calculations were done?

Here are five questions related to this topic:

  1. What is 535^3?
  2. What happens when you raise a number to the power of 0, such as 707^0?
  3. Can you explain why 04=00^4 = 0?
  4. How would you calculate 646^4?
  5. What is the general rule for exponents when the base is 1, like 1n1^n?

Tip: Any non-zero number raised to the power of 0 is always equal to 1!

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Math Problem Analysis

Mathematical Concepts

Exponents
Powers of Numbers

Formulas

a^n = a * a * a ... (n times)

Theorems

Any non-zero number raised to the power of 0 is 1
0 raised to any positive power is 0

Suitable Grade Level

Grade 6-8