HSCScience · Year 7 · Stage 4 Indices

Index Notation and Powers of 10

Outcome: MA4-IND-C-01 · Show working and explain the law or property used.

1. What is the base in 7⁴?
2. Which is the expanded form of 3⁴?
3. What is 2⁶?
4. Which equals 100,000?
5. Evaluate 20 − 2³ × 2.
6. Write 6⁴ in expanded form and evaluate it.
7. Write 2 × 2 × 2 × 5 × 5 in index form.
8. Evaluate 5 + 3² × 4.
9. Explain the difference between 4³ and 4 × 3.
10. Describe 5³ using the terms base, index, exponent and power.

Answers and reasoning

1. Answer

7. The repeated factor is the base, 7.

2. Answer

3 × 3 × 3 × 3. The index 4 means four factors of the base 3.

3. Answer

64. 2⁶ = 2 × 2 × 2 × 2 × 2 × 2 = 64.

4. Answer

10⁵. 10⁵ is 1 followed by five zeros.

5. Answer

4. Indices first: 2³ = 8; multiplication gives 16; then 20 − 16 = 4.

6. Model response

6 × 6 × 6 × 6 = 1,296.

7. Model response

2³ × 5².

8. Model response

Indices first: 3² = 9. Then 9 × 4 = 36 and 5 + 36 = 41.

9. Model response

4³ means 4 × 4 × 4 = 64, while 4 × 3 = 12. An index counts repeated factors.

10. Model response

The base is 5. The index, also called the exponent, is 3. The power 5³ means three factors of 5 and has value 125.

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