Edudel, Directorate of Education Govt. of NCT of Delhi Class 8 Mental Maths Question Bank Chapter 12 Exponents and Powers Questions Solution. In this chapter, there are total 40 math problems. We have given each questions solution step by step.
Edudel Class 8 Mental Maths Chapter 12 Exponents and Powers:-
1.) Simplify:
a.) (4)3
ANSWER:
(4)3 = 4 x 4 x 4
(4)3 = 64
b.) (3)4
ANSWER:
(3)4 = 3 x 3 x 3 x 3
(3)4 = 81
c.) (5)4
ANSWER:
(5)4 = 5 x 5 x 5 x 5
(5)4 = 625
d.) (7)3
ANSWER:
(7)3 = 7 x 7 x 7
(7)3 = 343
2.) Simplify:
a.) (2)-3
ANSWER:
We know, when power is odd number, answer we get is negative.
(2)-3 = 2 x 2 x 2
But power sign is negative.
(2)-3 = -8
b.) (1)-10
ANSWER:
We know, when power is even number, answer we get is positive.
(1)-10 = 1 x 1 x 1 x 1 x 1 x 1 x 1 x 1 x 1 x 1
(1)-10 = 1
c.) (6)-2
ANSWER:
We know, when power is even number, answer we get is positive.
(6)-2 = 6 x 6
(6)-2 = 36
d.) (8)-3
ANSWER:
We know, when power is odd number, answer we get is negative.
(8)-3 = 8 x 8 x 8
But power sign is negative.
(8)-3 = -512
3.) Simplify and write the answer in positive exponential form
a.) 43 /42
ANSWER:
We know,
am ÷ a n=a m-n
43 /42 = 4 3-2
43 /42 = 4
b.) (2-3 x 2-2) / 22
ANSWER:
We know,
am x a n=a m+n
(2-3 x 2-2) = 2 -3+ (-2)
(2-3 x 2-2) = 2 -5/ 22
am ÷ a n=a m-n
(2-3 x 2-2) / 22 = 2 -5-2
(2-3 x 2-2) / 22 = 2 -7
(2-3 x 2-2) / 22 = -128
c.) (2-4 x 41) / 22
ANSWER:
We know,
am x a n=a m+n
(2-4 x 41) = (2-4 x 22)
We know,
am x a n=a m+n
(2-4 x 22) = 2 -4+ 2
(2-4 x 22) = 2 -2
(2-4 x 22) / 22 =2 -2/ 22
(2-4 x 22) / 22 = -1
d.) (31 + 4-1 + 5-1 + 6-1)0
ANSWER:
We know,
When power is 1 then answer is always 1.
(31 + 4-1 + 5-1 + 6-1)0 = 1
4.) Simplify:
a.) 23 x 52 x 32
ANSWER:
23 x 52 x 32 = 2 x 2 x 2 x 5 x 5 x 3 x 3
23 x 52 x 32 = 8 x 25 x 9
23 x 52 x 32 = 1800
b.) 22 x 52 x 72
ANSWER:
22 x 52 x 72 = 2 x 2 x 5 x 5 x 7 x 7
22 x 52 x 72 = 4 x 25 x 49
22 x 52 x 72 = 4900
c.) (1/2)2 x (1/4)2 x (1/3)-2
ANSWER:
(1/2)2 x (1/4)2 x (1/3)-2 = 1/2 x 1/2 x 1/4 x 1/4 x 1/3 x 1/3
(1/2)2 x (1/4)2 x (1/3)-2 = 1/4 x 1/16 x 1/9
(1/2)2 x (1/4)2 x (1/3)-2 = 9/64
d.) (1/3)2 x (1/9)2 x 182
ANSWER:
(1/3)2 x (1/9)2 x 182
(1/9) = (1/32)
(1/32) x (1/34) x 182
1/9 x 1/81 x 324
(1/3)2 x (1/9)2 x 182 = 4/9
5.) Simplify:
(-5)-3 x (-7)2
ANSWER:
(-5)-3 x (-7)2
We write (-5)= (1/5)
And (-7) = (1/7)
(-5)-3 x (-7)2 = (1/5) x (1/5) x (1/5) x (1/7) x (1/7)
(-5)-3 x (-7)2 = -1/125 x 1/49
(-5)-3 x (-7)2 = – 49/125
6.) Simplify:
(-6)2 x (-5)3 / 23
ANSWER:
We write (-5)= (1/5)
And (-6) = (1/6)
(-6)2 x (-5)3 / 23 = (1/6) x (1/6) x (1/5) x (1/5) x (1/5) / 23
(-6)2 x (-5)3 / 23 = 1/36 x 1/125 / 8
(-6)2 x (-5)3 / 23 = -1125/2
7.) Find the value of a if, 7a = 495
ANSWER:
We have to find 7a = 495
We know,
49 = 72
7a = (72)5
We know,
(am) n = amxn
(72)5 = 710
7a = 710
Comparing,
a = 10
8.) Write (125)-3 in the exponential form as base 5
ANSWER:
We know,
125 = 53
(125)-3 = (53)-3
We know,
(am) n = amxn
(53)-3 = 5-9
(125)-3 = 5-9
9.) Simplify:
{(-2/3)2}3
ANSWER:
{(-2/3)2}3
We know,
(am) n = amxn
{(-2/3)2}3 = (-2/3)6
{(-2/3)2}3 = 64/729
10.) Find the value of m if, (5/7) m = 125/343
ANSWER:
(5/7) m = 125/343
We know,
125/343 = 53/73 = (5/7)3
(5/7) m = (5/7)3
Comparing,
m = 3
11.) Find the value of a/b if, (2/5)3 x (4/25)-2 = a/b
ANSWER:
(2/5)3 x (4/25)-2 = a/b
We write,
4 = 22
25 = 52
(2/5)3 x (22/52)-2 = a/b
(2/5)3 x (2/5)-4 = a/b
We know,
am x a n=a m+n
(2/5)3 x (2/5)-4 = (2/5)-1
(2/5)3 x (4/25)-2 = 5/2
12.) Simplify:
3-5 x 5-4 x 125 x 32
ANSWER:
3-5 x 5-4 x 125 x 32
We write,
125 = 53
3-5 x 5-4 x 53 x 32
We know,
am x a n=a m+n
5-4 x 53 = 5
3-5 x 32 = 3-3
3-5 x 5-4 x 53 x 32 = 5 x 3-3
3-5 x 5-4 x 53 x 32 = 5 x -27
3-5 x 5-4 x 53 x 32 = 1/135
13.) Simplify:
(x-1 + y-1) / x + y
ANSWER:
(x-1 + y-1) / x + y
We know,
(am x bm) = (a x b) m
(x-1 + y-1) = (x + y)-1
(x + y)-1/ x + y =
We know,
am ÷ a n=a m-n
(x + y)-1/ x + y = (x + y) -1 -1
(x + y)-1/ x + y = (x + y) -2
14.) Simplify: (2 -2 x 3 -2) / (6 -2)
ANSWER:
(2 -2 x 3 -2) / (6 -2)
We know,
(am x bm) = (a x b) m
(2 -2 x 3 -2) = (2 x 3)-2 = 6 -2
(2 -2 x 3 -2) / (6 -2) = 6 -2/ (6 -2)
(2 -2 x 3 -2) / (6 -2) = 1
15.) Simplify: (4 -1 + 29 0) / ((2)-2)
ANSWER:
We know,
a0 = 1
29 0 = 1
(4 -1 + 1) / ((2)-2)
(4 -1 + 29 0) / ((2)-2) = 5
16.) Find the value of (2p x 3p) if p = 2
ANSWER:
(2p x 3p) value of p = 2
(2p x 3p) = 2 x 2 x 32
(2p x 3p) = 4 x 9
(2p x 3p) = 36
17.) If (a) -8 = 1/ ((a) 2x)) then find the value of x.
ANSWER:
(a) -8 = 1/ ((a) 2x))
We know,
8 = 2 x 4
(a) -8 = 1/ ((a) 2x 4))
Comparing,
X = 4
18.) Simplify: 3 5 x 3 -2 x 3 4 x 3 -10
ANSWER:
We know,
am x a n=a m+n
3 5 x 3 -2 x 3 4 x 3 -10 = 3(5 -2 + 4-10)
3 5 x 3 -2 x 3 4 x 3 -10 = 3-3
3 5 x 3 -2 x 3 4 x 3 -10 = 1/27
19.) If 5 m x 125 m = (25) 2, then find the value of m.
ANSWER:
5 m x 125 m = (25) 2
We write,
125 = 53
25 = 52
5 m x 53m = 54
We know,
am x a n=a m+n
5 m x 53m = 5(m + 3m)
5 m x 53m =54m
54m = 54
Comparing,
4m = 4
m = 1
20.) If 7 n / (7 (2n)) = 1/7 then find the value of n.
ANSWER:
7 n / (7 (2n)) = 1/7
We know,
am ÷ a n=a m-n
7 n / (7 (2n)) = 7(n – 2n)
7 n / (7 (2n)) = 7-n
7-n= 1/7n
1/7n= 1/7
Comparing,
n = 1
21.) If (x 3 x x-2) 2 = 121 then find the value of x.
ANSWER:
(x3 x x-2)2 = 121
We know,
am x a n=a m+n
(x3 x x-2) = x
x2 = 121
We know,
112 = 121
X = 11
22.) Write 0.0081 in the standard form.
ANSWER:
0.0081 =
There are 4 decimal point.
We write,
0.0081 = 81 x 10-4
0.0081 = 8.1 x 10-3
23.) Write 1/10000000 in the standard form.
ANSWER:
We have to write 1/10000000 in the standard form.
1/10000000 = 1 x 10-7
24.) Write 4050000 in the standard form.
ANSWER:
We have to write4050000 in the standard form.
4050000 = 405 x 104
4050000 =40.5 x 105
4050000 =4.05 x 106
25.) If (5) (2x) = 625 then find the value of x.
ANSWER:
(5) (2x) = 625
We write,
625 = 54
(5) (2x) =54
Comparing,
2x = 4
X = 2
26.) Find the value of x if 27 2 x 27 3 = (3) x
ANSWER:
27 2 x 27 3 = (3) x
We know,
am x a n=a m+n
27 2 x 27 3 =27 5
we know,
27 = 33
We write,
27 5 = (33)5 = 315
315 =(3) x
Comparing,
X = 15
27.) Find the value of (a 3 x b 2) / a x b if a = 2 and b = 3.
ANSWER:
(a3 x b 2) / a x b
We put, a = 2 and b = 3.
(a3 x b 2) / a x b = (23 x 32) / 2 x 3
(2 3 x 3 2) / 2 x 3 = 8 x 9 / 6
(2 3 x 3 2) / 2 x 3 = 12
28.) Simplify: (√5) 5 / (√5) 3
ANSWER:
(√5) 5 / (√5) 3
We know,
am ÷ a n=a m-n
(√5) 5 / (√5) 3 = (√5)5 – 3
(√5) 5 / (√5) 3 =(√5)2
(√5) 5 / (√5) 3 = 5
29.) Write 9.432 x 10 – 4 in general form.
ANSWER:
We have to write 9.432 x 10 – 4 in general form.
9.432 x 10 – 4= 0.0009432
30.) Write 0.00032 x 10 5 in general form.
ANSWER:
We have to write0.00032 x 10 5 in general form.
0.00032 x 105 = 32
31.) If x = (3/2) 3 x (2/3) 4 them find the value of x 2
ANSWER:
x = (3/2) 3 x (2/3) 4
We have to find value of x2
(3/2) 3 x (2/3) 4 = 27/8 x (16/81)
(3/2) 3 x (2/3) 4 = 2/3
Value of x2= (2/3)2
Value of x2 = 4/9
32.) Simplify: (√1) 3 + 2 3 + 3 2 + 0 2
ANSWER:
We write,
√1 = (1 (1/2)) 3
1 (3/2) + 2 3 + 3 2 + 0 2
1 + 8 + 9
(√1) 3 + 2 3 + 3 2 + 0 2= 18
33.) Find the value of (1/27) (- 2/3)
ANSWER:
We have to find value of (1/27) (- 2/3)
We write,
(1/27) = (1/3)3
(1/27) (- 2/3) = ((1/3)3)(- 2/3)
(1/27) (- 2/3) =(1/3)-2
(1/27) (- 2/3) = 9
34.) Find the value of (125) (- 2/3)
ANSWER:
We have to find the value of (125) (- 2/3)
We write, 125 = 53
(125) (- 2/3) = (53)(- 2/3)
(53) (- 2/3) = 5-2
(125) (- 2/3) = 1/25
35.) Simplify: (√8) x (2) (1/2)
ANSWER:
We know,
(2) (1/2) = √2
(√8) x (√2)
√16
(√8) x (2) (1/2) = 4
36.) If 9 x = 1/27 then find the value of x.
ANSWER:
9 x = 1/27
We write,
9 = 32
27 = 33
9 x = 1/27 =
32x = (1/3)3
32x = (1/3) 3
32x = 3-3
Comparing,
2x = -3
x = -3/2
37.) Simplify: (32) (1/2) x (72) (1/2)
ANSWER:
(32) (1/2) x (72) (1/2)
We know,
(32) (1/2) = √32
(72) (1/2) =√72
(32) (1/2) x (72) (1/2)= √32 x √72
√32 x √72 = √16 x 2 x √36 x 2
= 4√2 x 6√2
= 24 x 2
(32) (1/2) x (72) (1/2)= 48
38.) Find the value of [6 3 + 8 3 + 10 3] (1/3)
ANSWER:
[6 3 + 8 3 + 10 3] (1/3)
[6 3 + 8 3 + 10 3](1/3) = (6 3) (1/3) + (8 3)(1/3) + (10 3)(1/3)
6 + 8 + 10
[6 3 + 8 3 + 10 3] (1/3)= 24
39.) Simplify: (x) (a2 – b 2) x (x)b2 -c2 x (x)c2 -a2
ANSWER:
(x) (a2 – b 2) x (x)b2 -c2 x (x)c2 -a2
We know,
am x a n=a m+n
(x) (a2 – b 2) x (x)b2 -c2 x (x)c2 -a2 = x (a2 – b 2 + b2 -c2 + c2 -a2)
(x) (a2 – b 2) x (x)b2 -c2 x (x)c2 -a2 = x 0
(x) (a2 – b 2) x (x)b2 -c2 x (x)c2 -a2= 1
40.) Simplify: (x) a + b. (x) b+c. (x) c+a / (x) a. (x)b .(x)c
ANSWER:
(x) a + b. (x) b+c. (x) c+a / (x) a. (x)b .(x)c
We know,
am x a n=a m+n
(x) a + b. (x) b+c. (x) c+a = (x)( a + b + b+c + c+a) = (x)2( a + b + c)
(x) a. (x)b .(x)c = (x)( a + b + c)
(x) a + b. (x) b+c. (x) c+a / (x) a. (x)b .(x)c = (x)2( a + b + c)/ (x)( a + b + c)
(x) a + b. (x) b+c. (x) c+a / (x) a. (x)b .(x)c = (x)( a + b + c)
41). Find the value of (2 – √3) if (√3) = 1.732
ANSWER:
(2 – √3) value of (√3) = 1.732
2 – 1.732 = 0.268
42.) Find the value of [(1) 1 + (2) 2 + (3) 3] (1/5)
ANSWER:
[(1) 1 + (2) 2 + (3) 3] (1/5)
(1 + 4 + 27) (1/5)
(32)(1/5)
We write,
32 = 25
(32) (1/5) = (25)(1/5) = 2
[(1) 1 + (2) 2 + (3) 3] (1/5) = 2
43.) Simplify: 4√3√√x
ANSWER:
4√3√√x = (((x1/2) 1/3)1/4))
4√3√√x = x 1/24
44.) Simplify: 4√3√x36
ANSWER:
4√3√x36 = (((x36)1/3)1/4)
4√3√x36 = x 3
45.) If (√5)/3) m = 1 – (2/3)2 then find the value of m.
ANSWER:
(√5)/3) m = 1 – (2/3)2
(√5)/3) m = 1 – 4/9
(√5)/3) m = 9 – 4 / 9
(√5)/3) m = 5 / 9
We take square root of 5 / 9
(√5)/3) m= (√5)/3)2
Comparing,
m = 2