1003032207
Level:
B
Let \( x=2^{4\sqrt2} \), \( y=4^{\frac{\sqrt2}2} \) and \( z=8^{-\frac{\sqrt2}3} \). Which two numbers are multiplicative inverses of each other?
\( y\), \( z \)
\( x\), \( y \)
\( x\), \( z \)
no two numbers
Expressions with exponents and radicals
1003032206
Level:
B
Simplifying the expression \( \frac{\left(\frac13\right)^{-3}\cdot27^{-2}}{9^{-5}\cdot\sqrt{3^4}} \) we will get:
\( 3^5 \)
\( 3^{-11} \)
\( 3^2 \)
\( 3^{-5} \)
1003032204
Level:
B
Order the numbers \( a=5^{\sqrt5} \), \( b=25\sqrt5 \), \( c=125^{\frac45} \), \( d=25^{1.1} \) from the smallest to the largest.
\( d < a < c < b \)
\( a < b < c < d \)
\( d < a < b < c \)
\( a < b < d < c \)
1003032205
Level:
B
Order the numbers \( a=4.5^{-2} \), \( b=\sqrt{0.4}^{\sqrt{12}} \), \( c=2.5^{-2.4} \), \( d=0.064 \) from the smallest to the largest.
\( a < d < c < b \)
\( d < a < c < b \)
\( a < d < b < c \)
\( c < a < b < d \)
1003032203
Level:
B
Writing the expression \( \frac{\sqrt[3]3\cdot9\cdot\sqrt{27}\cdot\sqrt[6]{81}}{81\cdot\sqrt[3]{\frac13}\cdot\sqrt[4]9} \) in the form of a power of \( 3 \), we will get:
\( 3^{\frac13} \)
\( 3^{-\frac56} \)
\( 3^{-\frac12} \)
\( 3^{-\frac23} \)
1003032202
Level:
B
Writing the expression \( \frac{(4x)^2\cdot(x:y)^{-2}}{(0.5)^{-4}\cdot y^{-1}}\), \( x\neq0\), \( y\neq0 \) in a simplified form, we will get:
\( y^3 \)
\( \frac12y^{-1} \)
\( 8y^3 \)
\( 256y^{-1} \)
1003032201
Level:
B
Let \( a=\left(\frac23\right)^{\sqrt7-\sqrt3} \) and \( b=\left(\frac23\right)^{\sqrt3+2} \).
Which of the following relations is true for \( a \) and \( b \)?
\( a>b \)
\( b>a \)
\( a=b \)
\( a\cdot b=\left(\frac23\right)^{2\sqrt7} \)
1003099211
Level:
A
Write the fraction \(\frac{2- \sqrt3}{2\sqrt3} \) in an equivalent form which does not contain a radical in the denominator.
\( \frac{2\sqrt3-3}6 \)
\( 0 \)
\( 1 \)
\( \frac{2\sqrt3-3}3 \)
1003099210
Level:
A
Write the fraction \( \frac{\sqrt[3]2}{\sqrt[3]3}\) in an equivalent form which does not contain a radical in the denominator.
\( \frac{\sqrt[3]{18}}3 \)
\( \frac{\sqrt[3]6}3 \)
\( \frac23 \)
\( \sqrt[3]6 \)
1003099209
Level:
A
Rationalize the denominator of \( \frac1{\sqrt[3]2} \).
\( 0.5\sqrt[3]4 \)
\( 0.5 \)
\( 0.5\sqrt[3]2 \)
\( 0.5\sqrt2 \)