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Solution: (a) 128 = 2 × 2 × 2 × 2 × 2 × 2 × 2 = 2 7

(b) 729 = 3 × 3 × 3 × 3 × 3 × 3 = 3 6
(c) 343 = 7 × 7 × 7 = 7 3
Example 8: Write the following in exponential form of their prime factors:

(a) 432 (b) 6750 (c) 10000

Solution: (a) 2 432 (b) 2 6750 (c) 2 10000
2 216 3 3375 2 5000
2 108 3 1125 2 2500
2 54 3 375 2 1250
625
5
3 27 5 125 5 125
3 9 5 25 5 25
3 5 5

432 = 2 × 2 × 2 × 2 × 3 6750 = 2 × 3 × 3 10000 = 2 × 2 × 2 × 2 × 5
4
× 3 × 3 = 2 × 3 3 × 3 × 5 × 5 × 5 = × 5 × 5 × 5 = 2 × 5 4
4
3
1
2 × 3 × 5 3
Knowledge Desk

The Bakhshali Manuscript, an ancient Indian mathematical text discovered near the village of Bakhshali in
Pakistan, dates back to approximately the 3rd to 4th century CE. This manuscript is renowned for its early
use of a place-value system and its sophisticated arithmetic and algebraic techniques. Among its contents,
the Bakhshali Manuscript contains procedures related to powers and roots. For example, it provides rules
for calculating squares and square roots, which can be seen as a precursor to the modern understanding of
exponents. While it does not explicitly use exponent notation, the manuscript’s methods reflect an advanced
grasp of mathematical concepts that laid the groundwork for later developments.

Practice Time 4A

1. Express the following in exponential form:

(a) 5 × 5 × 5 × 5 (b) 11 × 11 × 11 × 11 × 11
(c) (–7) × (–7) × (–7) × (–7) × (–7) (d) 2 × 2 × 2 × 3 × 3
(e) (–5) × (–5) × 7 × (–3) × (–3) × (–3) (f) (–1) × (–1) × 3 × 3

(g) (–10) × (–10) × (–10) × (–10) × (–10) × (–10)
2. Evaluate the following:
(a) 2 7 (b) 5 6 (c) (–7) 4 (d) (–5) 4 (e) (–3) 5
3. Express each of the following in exponential notation:

(a) 81 as power of 3 (b) 256 as power of 2 (c) 1331 as power of 11 (d) 1024 as power of 4
4. Write the following in exponential form of their prime factors:
(a) 256 (b) 432 (c) 2401 (d) 3200 (e) 15625
5. Which is greater in each of the following?
2
6
2
(a) (–2) or 6 2 (b) (–3) or (–2) 3 (c) 100 or 2 50
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