8th Grade > Mathematics
EXPONENTS AND POWERS MCQs
:
D
10−5
= 1105
= 1100000
When a number is multiplied with its multiplicative inverse, the result is 1. To make the given number, which is 1100000, equal to 1, we need to multiply it with 100000, which is the reciprocal of 1100000.
Therefore, 100000, or 105 is the multiplicative inverse of 10−5.
:
4×103+3×1+1×10−1+6×100=(4×1000)+(3×1)+110+(6×1)=4000+3+0.1+6=4009.1
:
C
4.95×105=4.95×100000=495000
:
B
Note that a0=1 for any a≠0
Thus, the value of 1000∘ is 1.
:
A
(−2)2×(−5)3=50m
⇒4×(−125)=50m
⇒−500=50m
⇒m=−10
:
A, B, and C
4x=64
⇒4x=43 (as 64 is 43 )
⇒x=3 (∵am = an if and only if m=n for a≠0,1,−1)
Since x=3, 22x = 64 , and 2x =6
:
A
The usual forms of the expressions 9×10−2 and 9×103 are given by 0.09 and 9000.
Thus, 9000 + 0.09 = 9000.09.
:
D
x5 × x4, for x = 2
Substituting 2 in place of x
= 25× 24
= 29 (∵am×an=am+n) = 512
:
B
We know that a−m=1am for any non-zero integer a and integer m.
⟹7−3=173
=17×7×7=1343
:
C
Multiplicative inverse of a non-zero x is 1x; so that when these two are multiplied, the product value is 1. Therefore, the multiplicative inverse of 10−7should be a number which when multiplied with 10−7 gives 1.
Let the multiplicative inverse of 10−7 be x.
Then, 10−7×x=1.
⇒x=110−7=107
(∵a−n=1an⟹1a−n=11an=an)
Thus, the multiplicative inverse of 10−7 is 107.