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.
\( a < d < c < b \)
\( d < a < c < b \)
\( a < d < b < c \)
\( c < a < b < d \)
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:
\( 3^5 \)
\( 3^{-11} \)
\( 3^2 \)
\( 3^{-5} \)
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
1003032208
Level:
B
Write the number \( \frac13\cdot9^{\pi+\frac12}:81^{2\pi} \) in the form of \( a^x \), where \( a \) is a natural number.
\( 3^{-6\pi} \)
\( 3^{6\pi} \)
\( 3^{-\frac12+3\pi} \)
\( 9^{-\frac12+3\pi} \)
1003032209
Level:
B
What is the value of \( \left(2^{\sqrt7-\sqrt2}\right)^{\sqrt7+\sqrt2} \)?
\( 32 \)
\( 2^{\sqrt{45}} \)
\( 2^9 \)
\( 1024 \)
1003032210
Level:
B
Which of the given numbers belongs to the interval \( (-5;5) \)?
\( 3\left(\sqrt{0.1}\right)^4\cdot\left(\sqrt3\right)^8 \)
\( \left(3\sqrt{5}\right)^2-\left(\sqrt2\right)^6 \)
\( \left(\sqrt3\right)^4-\left(\sqrt2\right)^4 \)
\( 3\left(\sqrt{0.1}\right)^4+\left(\sqrt3\right)^8 \)
1003034107
Level:
B
By computing \( 4^{11}\cdot4^{-11}\) we get:
\( 1 \)
\( 0 \)
\( 4^{22} \)
\( 16^{-121} \)
1003099408
Level:
B
The value of the expression \( \frac12\cdot\left[\frac{5\cdot\left(0.2+\frac35\right)^2}{3.2}\right]+\frac13 \) is:
\( \frac56 \)
\( \frac32 \)
\( \frac43 \)
\( \frac52 \)
1003099409
Level:
B
Simplifying \( \left( \frac1{\left( \sqrt[3]{729}+\sqrt[4]{256}+2 \right)^0} \right)^{-2} \) we get:
\( 1 \)
\( \frac1{15} \)
\( \frac1{225} \)
\( 15 \)
1003099410
Level:
B
The value of the multiplicative inverse of \( \left[ 2^{-2}+\left( \frac16 \right)^{-1} \right]^{\frac12} \) is:
\( \frac25 \)
\( \frac12+\sqrt6 \)
\( \frac4{25} \)
\( \frac52 \)