1003032108
Level:
B
Write the number \( 4^{-5}\cdot8^2 \) as \( 2^m \), where \( m \) is an integer.
\( 2^{-4} \)
\( 2^{-3} \)
\( 2^{-16} \)
\( 2^{-30} \)
Expressions with Exponents and Radicals
1003032107
Level:
A
The average distance of the Moon from Earth is \( 3.84\cdot10^8\,\mathrm{m} \), and the average distance of Earth from the Sun is \( 1.5\cdot10^{11}\mathrm{m} \). How many times further is it from Earth to the Sun than from Earth to the Moon?
about \( 390 \) times
about \( 39 \) times
\( 3\,900 \) times
about \( 4 \) times
1003032106
Level:
B
The value of the expression \( \frac{16^{\frac32}-16^{\frac54}}{40} \) is:
\( 0.8 \)
\( 0.4 \)
\( \frac1{20} \)
\( \frac1{40} \)
1003032105
Level:
B
Let \( a=5^{-1}\cdot\sqrt5 \), \( b=5^{-\frac32}\cdot25 \), \( c=125^{\frac14}:5^{-3} \), \( d=5^{\frac13}\cdot25^{-\frac13} \). Which of these numbers is the biggest?
\( c \)
\( a \)
\( b \)
\( d \)
1003032104
Level:
B
The number \(\sqrt[3]{(-2)^4}\cdot\left(\frac1{16}\right)^{-\frac23} \) equals:
\( 16 \)
\( -16 \)
\( -4 \)
\( 4 \)
1003032103
Level:
B
The number \( \sqrt[3]{\left(-27\right)^{-1}}\cdot81^{\frac34} \) equals:
\( -9 \)
\( -27 \)
\( 3 \)
\( 9 \)
1003032102
Level:
B
The number \( \frac{\left(1.4\cdot10^{6}\right)\cdot\left(5.4\cdot10^{-8}\right)}{\left(3.6\cdot10^{-3}\right)\left(3.5\cdot10^{-4}\right)} \) is \( k \)-times bigger than the number \( 3000 \) for:
\( k=20 \)
\( k=2 \)
\( k=6 \)
\( k=10 \)
1003032101
Level:
B
The product of the numbers \( \left(\sqrt[3]{25}\cdot\sqrt5\right)^{-1} \) and \( \sqrt[6]5\cdot625^{\frac14} \) equals:
\( 1 \)
\( \frac15 \)
\( \sqrt5 \)
\( 5 \)
1003032210
Level:
B
Which of the given numbers belongs to the interval \( (-5;5) \)?
\( 3\left(\sqrt{0.1}\right)^4\cdot\left(\sqrt3\right)^8 \)
\( \left(3\sqrt{5}\right)^2-\left(\sqrt2\right)^6 \)
\( \left(\sqrt3\right)^4-\left(\sqrt2\right)^4 \)
\( 3\left(\sqrt{0.1}\right)^4+\left(\sqrt3\right)^8 \)
1003032209
Level:
B
What is the value of \( \left(2^{\sqrt7-\sqrt2}\right)^{\sqrt7+\sqrt2} \)?
\( 32 \)
\( 2^{\sqrt{45}} \)
\( 2^9 \)
\( 1024 \)