2010004805
Level:
A
For \(x\in \mathbb{R}\),
\(x > 0\),
simplify the following expression.
\[
x\cdot \root{3}\of{x^{7}}
\]
\(x^{3}\root{3}\of{x}\)
\(x^{7}\root{3}\of{x}\)
\(x^{8}\root{3}\of{x}\)
\(x^2\root{3}\of{x^2}\)
Expressions with exponents and radicals
2010004804
Level:
B
For \(x\in \mathbb{R}\),
\(x > 0\),
simplify the following expression.
\[
\root{3}\of{x}\cdot \root{5}\of{x^{3}}
\]
\(\root{15}\of{x^{14}}\)
\(\root{5}\of{x}\)
\(\root{15}\of{x^{4}}\)
\(\sqrt{x}\)
2010004803
Level:
B
For \(x\in \mathbb{R}\),
\(x > 0\),
simplify the following expression.
\[
\root{5}\of{x^{4}} : \root{3}\of{x^2}
\]
\(\root{15}\of{x^{2}}\)
\(\root{15}\of{x^{22}}\)
\(\root{5}\of{x^{9}}\)
\(x\)
2010004802
Level:
B
The number \( \left( \sqrt{3+\sqrt5}+\sqrt{3-\sqrt5} \right)^2 \) equals:
\( 10 \)
\( 6 \)
\( 14 \)
\( 2\sqrt5 \)
2010004801
Level:
A
The value of the expression \( \sqrt[3]{81}-\sqrt{48}+5\sqrt{27}-\sqrt[3]{375} \) is equal to:
\( -2\sqrt[3]3+11\sqrt3 \)
\( 2\sqrt[3]9+11\sqrt3 - 5\sqrt[3]{15}\)
\(- 2\sqrt[3]3-\sqrt{3} \)
\( 2\sqrt[3]9-\sqrt3-5\sqrt[3]{15} \)
2010004707
Level:
B
The number \( \frac1{4^{2020}}\cdot(0.002)^{2020} \) equals:
\( (0.0005)^{2020} \)
\( \frac1{5000^{2020}} \)
\( (0.008)^{2020} \)
\( (0.005)^{2020} \)
2010004706
Level:
B
The multiplicative inverse of the number \( \frac{\sqrt{4^3}:8^{\frac13}}{\sqrt[3]4} \) is:
\( 2^{-\frac43} \)
\( 2^{\frac34} \)
\( 2^{\frac43} \)
\( 2^{-\frac13} \)
2010004705
Level:
B
Express the value of the expression \( \left(\frac32-3^{-2}\right)^{-1} \) as a decimal number.
\( 0.72 \)
\( 1.3\overline8\)
\( \frac{18}{25}\)
\( -0.1\overline3 \)
2010004704
Level:
B
The number \( \left(\frac{81^{-3}\cdot{16}^{-3}}{9^{-5}\cdot4^{-4}}\right)^{-2} \) equals:
\( 12^{4} \)
\( 6^4 \)
\( 6^{12} \)
\( \frac1{3^4\cdot2^{8}} \)
2010004703
Level:
B
Simplifying \( \left( \sqrt[5]{2\sqrt[3]8} \right)^{\frac52}\cdot \sqrt{4^{-1}} \) we get:
\( 1 \)
\( \sqrt2 \)
\( \frac{1}{\sqrt{2}} \)
\( 2 \)