Punjab State Board PSEB 7th Class Maths Book Solutions Chapter 13 Exponents and Powers Ex 13.1 Textbook Exercise Questions and Answers.
PSEB Solutions for Class 7 Maths Chapter 13 Exponents and Powers Ex 13.1
1. Fill in the blanks :
(i) In the expression 37, base = …………….. and exponent = ……………..
(ii) In the expression \(\left(\frac{2}{5}\right)^{11}\), base = …………….. and exponent = ……………..
Solution:
(i) 3, 7
(ii) \(\frac {2}{5}\), 11
2. Find the value of the following :
(i) 26
(ii) 93
(iii) 55
(iv) (-6)4
(v) \(\left(-\frac{2}{3}\right)^{5}\)
Solution:
(i) 26 = 2 × 2 × 2 × 2 × 2 × 2
= 64
(ii) 93 = 9 × 9 × 9
= 729
(iii) 55 = 5 × 5 ×5 × 5 × 5
= 3125
(iv) (-6)4 = -6 × -6 × -6 × -6
= 1296
(v) \(\left(-\frac{2}{3}\right)^{5}\) = \(\frac{-2}{3} \times \frac{-2}{3} \times \frac{-2}{3} \times \frac{-2}{3} \times \frac{-2}{3}\)
= \(-\frac{32}{243}\)
3. Express the following in the exponential form :
(i) 6 × 6 × 6 × 6
(ii) b × b × b × b
(iii) 5 × 5 × 7 × 7 × 7
Solution:
(i) 6 × 6 × 6 × 6 = 64
(ii) b × b × b × b = b4
(iii) 5 × 5 × 7 × 7 × 7 = 52 × 73
4. Simplify the following :
(i) 2 × 103
Solution:
2 × 103 = 2 × 10 × 10 × 10
= 2000
(ii) 52 × 32
Solution:
52 × 32 = 5 × 5 × 3 × 3
= 25 × 9
= 225
(iii) 32 × 104
Solution:
32 × 104 = 3 × 3 × 10000
= 90000
5. Simplify :
(i) (-3) × (-2)3
Solution:
(-3) × (-2)3 = -3 × -2 × -2 × -2
= -3 × -8
= 24
(ii) (-4)3 × 52
Solution:
(-4)3 × 52= -4 × -4 × -4 × 5 × 5
= 64 × 25
= -1600
(iii) (-1)99
Solution:
(-1)99 = -1
[(-1)odd number = -1]
(iv) (-3)2 × (-5)2
Solution:
(-3)2 × (-5)2 = -3 × -3 × – 5 × -5
= 9 × 25
= 225
(v) (-1)132
Solution:
(-1)132 = 1
[(-1)even number = +1]
6. Identify the greater number in each of the following :
(i) 43 or 34
Solution:
43 = 4 × 4 × 4 = 64
34 = 3 × 3 × 3 × 3 = 81
81 > 64
∴ 34 > 43.
(ii) 53 or 32
Solution:
53 = 5 × 5 × 5 = 125
32 = 3 × 3 = 9
125 > 9
∴ 53 > 32.
(iii) 23 or 82
Solution:
23 = 2 × 2 × 2 = 8
82 = 8 × 8 = 64
64 > 8
∴ 82 > 23.
(iv) 45 or 54
Solution:
45 = 4 × 4 × 4 × 4 × 4 = 1024
54 = 5 × 5 × 5 × 5 = 625
1024 > 625
∴ 45 > 54.
(v) 210 or 102
Solution:
210 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2
= 1024
102 = 10 × 10 = 100
1024 > 100
∴ 210 > 102
7. Write the following numbers as power of 2 :
(i) 8
Solution:
8 = 2 × 2 × 2
\(\begin{array}{c|c}
2 & 8 \\
\hline 2 & 4 \\
\hline 2 & 2 \\
\hline & 1
\end{array}\)
= 23
(ii) 128
Solution:
128 = 2 × 2 × 2 × 2 × 2 × 2 × 2
= 27
\(\begin{array}{l|l}
2 & 128 \\
\hline 2 & 64 \\
\hline 2 & 32 \\
\hline 2 & 16 \\
\hline 2 & 8 \\
\hline 2 & 4 \\
\hline 2 & 2 \\
\hline & 1
\end{array}\)
(iii) 1024
Solution:
1024 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2
=210
\(\begin{array}{l|l}
2 & 1024 \\
\hline 2 & 512 \\
\hline 2 & 256 \\
\hline 2 & 128 \\
\hline 2 & 64 \\
\hline 2 & 32 \\
\hline 2 & 16 \\
\hline 2 & 8 \\
\hline 2 & 4 \\
\hline 2 & 2 \\
\hline & 1
\end{array}\)
8. Write the following numbers as power of 3 :
(i) 27
Solution:
27 = 3 × 3 × 3
= 33
\(\begin{array}{l|l}
3 & 27 \\
\hline 3 & 9 \\
\hline 3 & 3 \\
\hline & 1
\end{array}\)
(ii) 2187
Solution:
2187 = 3 × 3 × 3 × 3 × 3 × 3 × 3
= 37
\(\begin{array}{l|l}
3 & 2187 \\
\hline 3 & 729 \\
\hline 3 & 243 \\
\hline 3 & 81 \\
\hline 3 & 27 \\
\hline 3 & 9 \\
\hline 3 & 3 \\
\hline & 1
\end{array}\)
9. Find the value of x in each of the following:
(i) 7x = 343
Solution:
343 =7 × 7 × 7 = 73
7x = 343
7x = 73
∴ x = 3
(ii) 9x = 729
Solution:
729 =9 × 9 × 9
= 93
9x = 729
9x = 93
∴ x = 3.
(iii) (-8)x = -512
Solution:
512 = 8 × 8 × 8
= 83
(-8)x = -512
(-8)x = (-8)3
∴ x = 3.
10. To what power (-2) should be raised to get 16 ?
Solution:
Let power raised be x
16 = 2 × 2 × 2 × 2
= 24
(-2)x = 24
(-2)x = (-2)4
[(-1)even number = +1]
∴ x = 4.
11. Write the prime factorization of the following numbers in the exponential form :
(i) 72
Solution:
72 = 2 × 2 × 2 × 3 × 3
= 23 × 32
\(\begin{array}{l|l}
2 & 72 \\
\hline 2 & 36 \\
\hline 2 & 18 \\
\hline 3 & 9 \\
\hline 3 & 3 \\
\hline & 1
\end{array}\)
(ii) 360
Solution:
360 = 2 × 2 × 2 × 3 × 3 × 5
= 23 × 32 × 51
\(\begin{array}{c|c}
2 & 360 \\
\hline 2 & 180 \\
\hline 2 & 90 \\
\hline 3 & 45 \\
\hline 3 & 15 \\
\hline 5 & 5 \\
\hline & 1
\end{array}\)
(iii) 405
Solution:
405 = 3 × 3 × 3 × 3 × 5
= 34 × 51
\(\begin{array}{l|l}
3 & 405 \\
\hline 3 & 135 \\
\hline 3 & 45 \\
\hline 3 & 15 \\
\hline 5 & 5 \\
\hline & 1
\end{array}\)
(iv) 648
Solution:
648 = 2 × 2 × 2 × 3 × 3 × 3 × 3
= 23 × 34
\(\begin{array}{c|c}
2 & 648 \\
\hline 2 & 324 \\
\hline 2 & 162 \\
\hline 3 & 81 \\
\hline 3 & 27 \\
\hline 3 & 9 \\
\hline 3 & 3 \\
\hline & 1
\end{array}\)
(v) 3600
Solution:
3600 = 2 × 2 × 2 × 2 × 3 × 3 × 5 × 5
= 24 × 32 × 52
\(\begin{array}{c|c}
2 & 3600 \\
\hline 2 & 1800 \\
\hline 2 & 900 \\
\hline 2 & 450 \\
\hline 3 & 225 \\
\hline 3 & 75 \\
\hline 5 & 25 \\
\hline 5 & 5 \\
\hline & 1
\end{array}\)