2000009403
Level:
B
The expression \( \sqrt[5]{1024}\) equals:
\(4\)
\(32\)
\(\sqrt{2}\)
\(25\)
Expressions with exponents and radicals
2010004701
Level:
B
The value of the multiplicative inverse of \( \left[ \left( \frac12 \right)^{-1} -5^{-2}\right]^{\frac12} \) is:
\( \frac57 \)
\( \sqrt2-\frac15 \)
\( \frac{25}{49} \)
\( \frac75 \)
2010004702
Level:
B
Simplify the fraction \( \frac{\sqrt[12]8\cdot\sqrt[20]{16}\cdot\sqrt[5]{15}}{\sqrt[5]{30}} \).
\( \sqrt[4]2 \)
\( \frac1{\sqrt[4]2} \)
\( 1 \)
\( 2 \)
2010004703
Level:
B
Simplifying \( \left( \sqrt[5]{2\sqrt[3]8} \right)^{\frac52}\cdot \sqrt{4^{-1}} \) we get:
\( 1 \)
\( \sqrt2 \)
\( \frac{1}{\sqrt{2}} \)
\( 2 \)
2010004704
Level:
B
The number \( \left(\frac{81^{-3}\cdot{16}^{-3}}{9^{-5}\cdot4^{-4}}\right)^{-2} \) equals:
\( 12^{4} \)
\( 6^4 \)
\( 6^{12} \)
\( \frac1{3^4\cdot2^{8}} \)
2010004705
Level:
B
Express the value of the expression \( \left(\frac32-3^{-2}\right)^{-1} \) as a decimal number.
\( 0.72 \)
\( 1.3\overline8\)
\( \frac{18}{25}\)
\( -0.1\overline3 \)
2010004706
Level:
B
The multiplicative inverse of the number \( \frac{\sqrt{4^3}:8^{\frac13}}{\sqrt[3]4} \) is:
\( 2^{-\frac43} \)
\( 2^{\frac34} \)
\( 2^{\frac43} \)
\( 2^{-\frac13} \)
2010004707
Level:
B
The number \( \frac1{4^{2020}}\cdot(0.002)^{2020} \) equals:
\( (0.0005)^{2020} \)
\( \frac1{5000^{2020}} \)
\( (0.008)^{2020} \)
\( (0.005)^{2020} \)
2010004802
Level:
B
The number \( \left( \sqrt{3+\sqrt5}+\sqrt{3-\sqrt5} \right)^2 \) equals:
\( 10 \)
\( 6 \)
\( 14 \)
\( 2\sqrt5 \)
2010004803
Level:
B
For \(x\in \mathbb{R}\),
\(x > 0\),
simplify the following expression.
\[
\root{5}\of{x^{4}} : \root{3}\of{x^2}
\]
\(\root{15}\of{x^{2}}\)
\(\root{15}\of{x^{22}}\)
\(\root{5}\of{x^{9}}\)
\(x\)