1003034108
Level:
C
Give the result of the gradual exponentiation \(\left(\left(\left(\left(2\right)^2\right)^0\right)^3\right)^4\):
\( 1 \)
\( 0 \)
\( 4^{12} \)
\( 2^9 \)
Expressions with exponents and radicals
1003034107
Level:
B
By computing \( 4^{11}\cdot4^{-11}\) we get:
\( 1 \)
\( 0 \)
\( 4^{22} \)
\( 16^{-121} \)
1003034106
Level:
A
The value of the expression \( \frac{\sqrt[3]{81}}{\sqrt[3]3} \) is:
\( 3 \)
\( 3\sqrt3 \)
\( \frac9{\sqrt[3]3} \)
\( 27 \)
1003034104
Level:
A
Evaluating the expression \( \frac13\sqrt[3]4\cdot\sqrt[3]2 \) we get:
\( \frac23 \)
\( \frac83 \)
\( \frac26 \)
\( \frac33 \)
9000085602
Level:
C
Evaluate the following numbers and round to the nearest tens.
\[
\left [(2^{2})^{2}\right ]^{2}
\]
\(260\)
\(510\)
\(120\)
\(60\)
9000079207
Level:
B
Assuming \(x\not \in \{0;1;3\}\),
simplify the following expression.
\[
\frac{x^{2} - 9}
{x^{2} - x}\cdot \left (\frac{x^{2} - 3x}
{x - 1} \right )^{-1}
\]
\(\frac{x+3}
{x^{2}} \)
\(\frac{x-3}
{x^{2}} \)
\(\frac{x+3}
{2x} \)
\(\frac{x+3}
{x} \)
9000079209
Level:
C
Evaluate the following expression at \(x = 4\).
\[
\frac{x^{-\frac{1}
{2} }}
{x^{-2} - x^{-1}}
\]
\(-\frac{8}
{3}\)
\(\frac{31}
{3} \)
\(\frac{8}
{3}\)
\(6\)
9000010506
Level:
B
For \(x\in \mathbb{R}\),
\(x > 0\),
simplify the following expression.
\[
x\cdot \root{}\of{x}\cdot \root{3}\of{x}
\]
\(x\root{6}\of{x^{5}}\)
\(\root{6}\of{x^{3}}\)
\(\root{}\of{x}\)
\(x^{5}\root{6}\of{x^{5}}\)
9000010507
Level:
A
For \(x\in \mathbb{R}\),
\(x > 0\),
simplify the following expression.
\[
x^{3} : \root{}\of{x}
\]
\(x^{2}\root{}\of{x}\)
\(x^{3}\root{}\of{x}\)
\(\root{}\of{x^{3}}\)
\(\root{6}\of{x}\)
9000010510
Level:
B
For \(x\in \mathbb{R}\),
\(x > 0\),
simplify the following expression.
\[
\root{3}\of{x} : \root{6}\of{x}
\]
\(\root{6}\of{x}\)
\(\root{}\of{x}\)
\(\root{3}\of{x^{2}}\)
\(x\)