Exponents and Scientific Notation Quiz

Grade 8 · Math · Quiz

Demonstrate your mastery of exponent rules and scientific notation.

Questions

1. Simplify: x^6 ÷ x^2

   1. x^3
   2. x^4
   3. x^8
   4. x^12
   Show answer

   Answer: x^4

   Quotient rule: x^6 ÷ x^2 = x^(6-2) = x^4.

2. What is 0.00072 written in scientific notation?

   1. 7.2 × 10^4
   2. 7.2 × 10^(-4)
   3. 72 × 10^(-5)
   4. 7.2 × 10^(-3)
   Show answer

   Answer: 7.2 × 10^(-4)

   0.00072 requires moving the decimal 4 places right, giving a negative exponent of -4.

3. Simplify (2^3)^2.

   1. 2^5
   2. 2^6
   3. 2^9
   4. 4^6
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   Answer: 2^6

   Power rule: (2^3)^2 = 2^(3×2) = 2^6 = 64.

4. What is the value of 10^(-3)?

   1. 1000
   2. -1000
   3. 0.001
   4. 0.01
   Show answer

   Answer: 0.001

   10^(-3) = 1/10^3 = 1/1000 = 0.001.

5. Multiply: (3 × 10^4) × (2 × 10^3)

   1. 6 × 10^7
   2. 5 × 10^7
   3. 6 × 10^12
   4. 6 × 10^1
   Show answer

   Answer: 6 × 10^7

   Multiply decimals: 3 × 2 = 6. Add exponents: 10^4 × 10^3 = 10^7. Result: 6 × 10^7.

6. Which expression equals 1?

   1. 5^1
   2. 5^(-1)
   3. 5^0
   4. 0^5
   Show answer

   Answer: 5^0

   Any nonzero number raised to the power of 0 equals 1.

7. 2^3 × 3^3 = 6^3

   Show answer

   Answer: True

   2^3 × 3^3 = 8 × 27 = 216 = 6^3. This works because (ab)^n = a^n × b^n.

8. In standard form, 3.8 × 10^6 = _____

   Show answer

   Answer: 3800000

   Move the decimal 6 places to the right: 3.8 × 10^6 = 3,800,000.

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