Chapter 2. Exponents and Radicals
Chapter 2. Exponents and Radicals
Chapter 2. Exponents and Radicals
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MODULE - 1<br />
Algebra<br />
<strong>Exponents</strong> <strong>and</strong> <strong>Radicals</strong><br />
Example <strong>2.</strong>3: Express each of the following in exponential notation <strong>and</strong> write the base<br />
<strong>and</strong> exponent in each case.<br />
Notes<br />
125<br />
(i) 4096 (ii) 729<br />
(iii) – 512<br />
Solution: (i) 4096 = 4 × 4 × 4 × 4 × 4 × 4 Alternatively 4096 = (2) 12<br />
= (4) 6 Base = 2, exponent =12<br />
Here, base = 4 <strong>and</strong> exponent = 6<br />
125 5 5 5 ⎛ 5 ⎞<br />
(ii) = × × = ⎜ ⎟⎠ 729 9 9 9 ⎝ 9<br />
⎛ 5 ⎞<br />
Here, base = ⎜ ⎟ <strong>and</strong> exponent = 3<br />
⎝ 9 ⎠<br />
(iii) 512 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 = 2 9<br />
Here, base = 2 <strong>and</strong> exponent = 9<br />
Example <strong>2.</strong>4: Simplify the following:<br />
3<br />
⎛ 3 ⎞<br />
⎜ ⎟<br />
⎝ 2 ⎠<br />
3<br />
⎛ 4 ⎞<br />
× ⎜ ⎟<br />
⎝ 3 ⎠<br />
4<br />
3<br />
⎛ 3 ⎞ 3 3 3 3<br />
Solution: ⎜ ⎟ = × × =<br />
3<br />
⎝ 2 ⎠ 2 2 2 2<br />
4<br />
⎛ 4 ⎞ 4<br />
Similarly ⎜ ⎟ =<br />
4<br />
⎝ 3 ⎠ 3<br />
⎛ 3 ⎞<br />
⎜ ⎟<br />
⎝ 2 ⎠<br />
3<br />
4<br />
3<br />
⎛ 4 ⎞<br />
× ⎜ ⎟<br />
⎝ 3 ⎠<br />
4 3 4<br />
3 4<br />
=<br />
3 ×<br />
4<br />
=<br />
2<br />
3<br />
3<br />
3 16×<br />
16<br />
× =<br />
4<br />
8 3<br />
Example <strong>2.</strong>5: Write the reciprocal of each of the following <strong>and</strong> express them in exponential<br />
form:<br />
32<br />
3<br />
(i) 3 5<br />
⎛ 3 ⎞<br />
(ii) ⎜ ⎟⎠<br />
⎝ 4<br />
2<br />
(iii)<br />
9<br />
⎛ 5 ⎞<br />
⎜ − ⎟⎠<br />
⎝ 6<br />
42<br />
Mathematics Secondary Course
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