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Published on: 26/07/2019
Exponents and Powers
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Questions + Answers key
Take MCQ Mathematics Test
1.
Write each of the following in standard form: 0.00001278
2.
Write each of the following in standard form: 0.0016
3.
Expand the following numbers using exponents.
1025.63
4.
Find the multiplicative inverse of the following:
10-100
5.
Find the multiplicative inverse of the following:
5-3
6.
Express 2.0001 \(\times\) 109 in usual form.
7.
Write the following in standard form: 34500000.
8.
Write the following in standard form: 0.000000456
9.
Express each of the following numbers in standard form.
0.0005
10.
Find the standard form of the number 0.0005+0.0085.
11.
Astronomy The table shows the mass of the planets, the Sun and the Moon in our solar system.
| Celestial Body | Mass (kg) | Mass (kg) in Standard Notation |
|---|---|---|
| Sun | 1990000000000000000000000000000 | |
| Mercury | 330000000000000000000000 | |
| Venus | 4870000000000000000000000 | |
| Earth | 5970000000000000000000000 | |
| Mars | 642000000000000000000000000000 | |
| Jupiter | 1900000000000000000000000000 | |
| Saturn | 568000000000000000000000000 | |
| Uranus | 86800000000000000000000000 | |
| Neptune | 102800000000000000000000000 | |
| Pluto | 12700000000000000000000 | |
| Moon | 73500000000000000000000 |
(a) Write the mass of each celestial body in standard notation.
(b) Arrange the planets and the Moon according to their mass from least to greatest.
(c) Which planet has same mass as the Earth?
12.
\({ \left[ { \left( \frac { 1 }{ 2 } \right) }^{ -1 }+{ \left( \frac { 2 }{ 3 } \right) }^{ 2 }-{ \left( \frac { 3 }{ 4 } \right) }^{ 0 } \right] }^{ 2 }\) is equal to:
\(\frac { 81 }{ 484 } \)
\(\frac { 81 }{ 169 } \)
\(\frac { 169 }{ 81 } \)
\(\frac { 16 }{ 81 } \)
13.
1 micron is equal to \(\frac { 1 }{ 1000000 } m\). Which of the following is its standard form?
1.1 \(\times\) 10-5
1.6 \(\times\) 10-5
0.1 \(\times\) 10-6
1.0 \(\times\) 10-6
14.
For Which of the following m = 8?
\(\frac { { 5 }^{ m }\div { 5 }^{ -3 } }{ { 5 }^{ 2 } } ={ 5 }^{ 3 }\)
\(-\frac { { 5 }^{ m }\div { 5 }^{ -3 } }{ { 5 }^{ 3 } } ={ 5 }^{ 2 }\)
\(\frac { { 5 }^{ m }\div { 5 }^{ 3 } }{ { 5 }^{ 2 } } ={ 5 }^{ 3 }\)
\(\frac { 5\div { 5 }^{ -2 } }{ { 5 }^{ 2 } } ={ 5 }^{ 3 }\)
15.
Which of the following is the used form of 5.05 \(\times\) 106?
505000
505000000
5050000
50500000
16.
Which of the following is the standard form of 0.00001275?
1.275 \(\times\) 10-5
1.275 \(\times\) 10-5
127.5 \(\times\) 10-7
127.5\(\times\) 107
17.
The value of 52 x 5-2 is
1
5
54
5-4
18.
The reciprocal of \((\frac{3}{7})^{-1}\)is
\(\frac{7}{3}\)
\(-\frac{3}{7}\)
\(-\frac{7}{3}\)
\(\frac{3}{7}\)
19.
The value of \(\frac{1}{9^{-2}}\) is
27
81
-81
18
20.
5-2 can be written as
\(\frac{1}{5}\)
\(\frac{1}{5^{2}}\)
52
-\(\frac{2}{5}\)
21.
In 3n, n is known as
base
constant
exponent
variable
22.
The value of [2-1 +3-1 +4-1 +5-1]0 is _____________
23.
The standard form of \(\frac{1}{10000000000}\) is ____________
24.
The standard form of 12345000000 is ____________
25.
The value of(4-1 + 2-1 + 3-1)1 is _____________
26.
1000 = ____________
27.
\((\frac{7}{9})^{-2}\times (\frac{7}{9})^{-8}=(\frac{7}{9})^{16}\)
28.
\(a^{m}\times a^{n}=(ab)^{mn}\)
29.
\((-\frac{9}{2})^{0}=0\)
30.
The value of \(\frac{1}{7^{-3}}\) is equal to 216.
31.
(-8)-2 x(-8)-3 =(-8)-5
32.
The multiplicative inverse of 10-100
33.
The standard form of \(\frac { 1 }{ { 10 }^{ 100 } } \)
34.
(25÷28) X 2-7
35.
\(\frac{49\times z^{-3}}{7^{-3}\times 10\times z^{-5}}(z\ne0)\)
36.
\(((\frac{-2}{3})^{-2})^{3}\times (\frac{1}{3})^{-4}\times 3^{-1}\times \frac{1}{6}\)
1.
1.278 \(\times\)10-5
2.
1.6 \(\times\) 10-3
3.
We have, 1025.63 = 1x 1000 + 0 x 100 + 2 x 10 + 5 x 1+\(\frac{6}{10}+\frac{3}{100}\)
=1\(\times 10^{3}+2\times10^{1}+5\times 10^{0}+6\times 10^{-1}+3\times 10^{-2}\)
4.
Multiplicative inverse of 10-100 is 10100.
5.
Multiplicative inverse of 5-3 is 53.
6.
We have
\(2.0001\times { 10 }^{ 9 }=\frac { 20001 }{ 10000 } \times 1000000000\)
= 20001 \(\times\) 100000
= 2000100000
Thus, 2.0001 \(\times\) 109 = 2000100000
7.
34500000 - 345 \(\times\) 100000
= 3.45 \(\times\) 100 \(\times\) 100000
= 3.45 \(\times\) 102 \(\times\) 105
= 3.45 \(\times\) 102+5
= 3.45 \(\times\) 107
Thus, 34500000 = 3.45 \(\times\) 107
8.
0.000000456=\(\frac { 456 }{ 1000000000 } \)
\(=\frac { 4.56 }{ 10000000000 } \times 100=\frac { 4.56 }{ 10000000 } \)
\(=\frac { 4.56 }{ 10^{ 7 } } =4.56\times { 10 }^{ -7 }\)
Thus, 0.000000456 = 4.56 \(\times\) 10-7
9.
5 x 10-4
10.
9x 10-3
11.
(a) Mass of each celestial body in standard in notation is given below.
Mass of Sun = 1.99 x 1030 kg
Mass of Mercury = 3.3 x 1023 kg
Mass of Venus = 4.870 x 1024 kg
Mass of Earth = 5.970 x 1024 kg
Mass of Mars = 6.42 x 1029 kg
Mass of Jupiter = 1.9 x 1027 kg
Mass of Saturn = 5.68 x1026 kg
Mass of Uranus = 8.68 x 1025 kg
Mass of Neptune = 1.02 x 1026 kg
Mass of Pluto = 1.27 x 1022 kg
Mass of Moon = 7.35 x 1022 kg
(b) On observing the masses of the all given planets and the Moon in the exponent form, we see that the order of planets and the Moon by mass from least to greatest is Pluto < Moon < Mercury < Venus < Earth < Uranus < Neptune < Saturn < Jupiter < Mars
(c) ஃ Mass of Earth = 5.970 X1024 kg and mass of Venus = 4.870 x 1024 kg ,
Thus, we can say that planet Venus has about same mass as the Earth.
12.
(b)
\(\frac { 81 }{ 169 } \)
13.
(d)
1.0 \(\times\) 10-6
14.
(c)
\(\frac { { 5 }^{ m }\div { 5 }^{ 3 } }{ { 5 }^{ 2 } } ={ 5 }^{ 3 }\)
15.
(c)
5050000
16.
(a)
1.275 \(\times\) 10-5
17.
(a)
1
18.
(d)
\(\frac{3}{7}\)
19.
(b)
81
20.
(b)
\(\frac{1}{5^{2}}\)
21.
(c)
exponent
22.
( )
1
23.
( )
10-10
24.
( )
1.2345 x 1010
25.
( )
\(\frac{12}{13}\)
26.
( )
1
27.
(b)
28.
(b)
29.
(b)
30.
(b)
31.
(a)
32.
( )
10100
33.
( )
10-100
34.
( )
2-10
35.
( )
\(\frac{7^{5}}{10}z^{2}\)
36.
( )
\(\frac{3^{8}}{2^{7}}\)
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