2010005606
Level:
A
The sum of \( 4^{50}+4^{50}+4^{50}+4^{50} \) equals:
\( 4^{51} \)
\( 4^{54} \)
\( 4^{200} \)
\( 16^{50} \)
Expressions with exponents and radicals
2010005605
Level:
A
Calculate \( \left(2\sqrt{72}-3\sqrt{50}+2\sqrt{32}\right)^2 \).
\( 50 \)
\( 100 \)
\( 5 \)
\( 25 \)
2010005604
Level:
A
Simplifying \( \frac23\sqrt{27} + \sqrt{81} - \sqrt{12} + \frac14\sqrt{48} \) you get:
\( 9+\sqrt3 \)
\( 3+3\sqrt{3} \)
\( 9+5\sqrt{3} \)
\( 15-\sqrt{3} \)
2010005603
Level:
A
Rationalize the denominator of \( \frac1{\sqrt[3]5} \).
\( \frac{\sqrt[3]{25}}{5} \)
\( \frac15 \)
\( \frac{\sqrt[3]{5}}{5} \)
\( \frac{\sqrt5}5 \)
2010005602
Level:
A
Rationalize the denominator of \( \frac{\sqrt{3}-3}{\sqrt 3} \).
\(1- \sqrt 3 \)
\( -3 \)
\( 1+\sqrt3 \)
\( 1-\sqrt3\)
2010005601
Level:
A
The mean distance of Uranus from the Sun is \( 4.53\cdot10^{12}\,\mathrm{m} \), and the mean distance of Mercury from the Sun is \( 5.79\cdot10^{10}\,\mathrm{m} \). How many times farther Uranus from the Sun than Mercury is?
about \( 78 \) times
about \( 780 \) times
\( 130\) times
about \( 8\) times
2010004809
Level:
C
Evaluate the following expression at \(x = 9\).
\[
\frac{x^{-2}}
{x^{-\frac{1}{2}} - x^{-1}}
\]
\(\frac{1}
{18}\)
\(-\frac{1}
{18} \)
\(\frac{27}
{2}\)
\(-\frac{27}
{8}\)
2010004808
Level:
B
Assuming \(x\not \in \{-4;-1;0;4\}\),
simplify the following expression.
\[
\left(\frac{x+1}
{x^{2} +4x}\right)^{-1}\cdot \frac{x^{2} +x}
{x^2 - 16}
\]
\(\frac{x^2}
{x-4} \)
\(\frac{x^2}
{x+4} \)
\(\frac{2x}
{x-4} \)
\(\frac{x}
{x-4} \)
2010004807
Level:
B
Write the number \(\root{12}\of{5^{-4}}\)
as a power with a rational exponent.
\(5^{-\frac{1}
{3} }\)
\(5^{\frac{1}
{3} }\)
\(5^{3}\)
\(5^{-3}\)
2010004806
Level:
B
Simplify the expression \(0.3^{\frac{4}
{5} }\cdot 0.3^{-\frac{3}
{10} }\)
and write the result using a root.
\(\sqrt{0.3}\)
\(\root{5}\of{0.3}\)
\(\root{10}\of{0.3^{7}}\)
\(\root{3}\of{0.3^8}\)