Chapter 13 Exponents and Powers Exercise 13.1
Question 1: Find the value of:
(a) 2⁶
Answer:
= 2 x 2 x 2 x 2 x 2 x 2
= 64
(b) 9³
Answer:
= 9 x 9 x 9
= 729
(c) 11²
Answer:
= 11 x 11
= 121
(d) 5⁴
Answer:
= 5 x 5 x 5 x 5
= 625
Question 2: Express the following in exponential form:
(a) 6 x 6 x 6 x 6
Answer:
= 6⁴
(b) t x t
Answer:
= t²
(c) b x b x b x b
Answer:
= b⁴
(d) 5 x 5 x 7 x 7 x 7
Answer:
= 5² x 7³
(e) 2 x 2 x a x a
Answer:
= 2² x a²
(f) a x a x a x c x c x c x c x d
Answer:
= a³ x c⁴ x d¹
Question 3: Express each of the following numbers using exponential notation:
(a) 512
Answer:
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhKPEBQjUMaQlScM84oIPANa7tDIqBizFFBYm_YgVyiTo4Aq8wPu0TOPxrplZNGAKfbYBpaTBst83zc2Nzkqc2Is7k4oOXlAE_O2HHe_mSq44Wu-F2j4wnovzMUeXsVLALiVl8kMXsucRXd/s16000/1.png)
(ii) 343
Answer:
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg9q0uG1kpe4JRDZ3eTksw-37KwAQnlIfW7iykEPwsQFIHW7s_dRYFf5m8OEtna7ceI5nPOPrOa8NX4xvR_RDa3FvfqqMmupxuYS1iQ681JpP2V4a5rBCgt8tH1FmDBrV_OpWiqpIgDq53j/s16000/2.png)
Answer:
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEicq0q4LpC7JZYST0fDbCdODXxo0pYdtmMoyVUisxNa11MLYeM5-YF2f9KS8FQeoW0U7QZ3VrZ2TGyIjdlVVbEagSBISzppjMaalYwN4BNP8t9RoaHayl1erc25BAd2iGTE8-mWRygSWT30/s16000/3.png)
Answer:
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgYIqFAxeQSO7hhgqUM_bfoedVTep5IP6iu-fS52yICFYyTLudpI2rWEPOXbefzhdFHSbibkNMYPQfDtQL_uRqb6YdMVUTfxKkP-JTB8ah8IiAzvZA8KRfe2bH-RELBtdyY0MTA9RqOgHIr/s16000/4.png)
Question 4: Identify the greater number, wherever possible, in each of the following?
(i) 4³ or 3⁴
Answer:
4³ = 4 x 4 x 4
= 64
3⁴ = 3 x 3 x 3 x 3
= 81
64 < 81
Therefore, 3⁴ is greater.
(ii) 5³ or 3⁵
Answer:
5³ = 5 x 5 x 5
= 125
3⁵ = 3 x 3 x 3 x 3 x 3
= 243
125 < 243
Therefore, 3⁵ is greater.
(iii) 2⁸ or 8²
Answer:
2⁸ = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2
= 256
8² = 8 x 8
= 64
256 < 64
Therefore, 2⁸ is greater.
(iv) 100² or 2¹⁰⁰
Answer:
100² = 100 x 100
= 10000
2¹⁰ = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2
= 1024¹⁰
10000 < 1024¹⁰
Therefore, 2¹⁰⁰ is greater.
(v) 2¹⁰ or 10²
Answer:
2¹⁰ = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2
= 1024
10² = 10 x 10
= 100
1024 < 100
Therefore, 2¹⁰ is greater.
Question 5: Express each of the following as product of powers of their prime factors:
(i) 648
Answer:
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhHv3qp08D6u60Bmw_9yykrNal0x4hPnATBsCXjllSEJg9tolqdKAWwZD0lPOH2ctkxKDcMJoelj9gI7YVcQJTuJ9g6iPt-ezYO_L-vQtEhT3zt2-mAuOYfXid0OYUXIf2aubTAjk77qGGN/s16000/1.jpg)
(ii) 405
Answer:
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh0N8_eiN9KyYVxzdHApm0iC29ys1nkkB2moM1HSylFgUX_nn1Fmu2PmjdXLzW7ab15QRfER7kXEsG1JzoLzpisTS9VdcDU7fy9TrHQrtmUOrestyZl41eh7fSGByNzUC7mjfQZH2k9jbVE/s16000/2.jpg)
(iii) 540
Answer:
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEisGhkZEP7sxK-oEbgVRO1yAhgL8_yBTs6Fwxzjtyv2LIaVFkt0Qb22_KFa3EP1ooPxEntpmYzHbYdM8umcAdvAgs2Pt0sj2p8g7qMuzvjCWjf3jTgzONOyAu0MdmMHL_walssTuPYh51-Q/s16000/3.jpg)
(iv) 3,600
Answer:
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj3fTbODCxoWmMyxK0OxkOt7oOVhLCJGFwr9DXweQCBte_ajZOOyU8RpBZ9DRSXppAXW6VSb5-h8T4LiJaB_4krL5ISKDPjoykU4QNtOh4fzbfO1BzOTi6sBqRSfOmXAE7SXbKZzbmv2Nqg/s16000/4.jpg)
Question 6: Simplify:
(i) 2 × 10³
Answer:
= 2 × 10 × 10 × 10
= 2 × 1000
= 2000
(ii) 7² × 2²
Answer:
= 7 × 7 × 2 × 2
= 49 × 4
= 196
(iii) 2³ × 5
Answer:
= 2 × 2 × 2 × 5
= 8 × 5
= 40
(iv) 3 × 4⁴
Answer:
= 3 × 4 × 4 × 4 × 4
= 3 × 256
= 768
(v) 0 × 10²
Answer:
= 0 × 10 × 10
= 0 × 100
= 0
(vi) 5² × 3³
Answer:
= 5 × 5 × 3 × 3 × 3
= 25 × 27
= 675
(vii) 2⁴ × 3²
Answer:
= 2 × 2 × 2 × 2 × 3 × 3
= 16 × 9
= 144
(viii) 3² × 10⁴
Answer:
= 3 × 3 × 10 × 10 × 10 × 10
= 9 × 10000
= 90000
Question 7: Simplify:
(i) (-4)³
Answer:
= -4 × -4 × -4
= -64
(ii) (-3) × (-2)³
Answer:
= -3 × -2 × -2 × -2
= -3 × -8
= 24
(iii) (-3)² × (-5)²
Answer:
= -3 × -3 × -5 × -5
= 9 × 25
= 225
(iv) (-2)³ × (-10)³
Answer:
= -2 × -2 × -2 × -10 × -10 × -10
= -8 × -1000
= 8000
Question 8: Compare the following numbers:
(i) 2.7 × 10¹² ; 1.5 × 10⁸
Answer:
2.7 × 10¹² ____ 1.5 × 10⁸
Comparing the exponents of base 10.
2.7 × 10¹² > 1.5 × 10⁸
(ii) 4 × 10¹⁴ ; 3 × 10¹⁷
Answer:
4 × 10¹⁴ ____ 3 × 10¹⁷
Comparing the exponents of base 10.
4 × 10¹⁴ < 3 × 10¹⁷
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