2010004804
Level:
B
For \(x\in \mathbb{R}\),
\(x > 0\),
simplify the following expression.
\[
\root{3}\of{x}\cdot \root{5}\of{x^{3}}
\]
\(\root{15}\of{x^{14}}\)
\(\root{5}\of{x}\)
\(\root{15}\of{x^{4}}\)
\(\sqrt{x}\)
Expressions with powers and roots
2010004806
Level:
B
Simplify the expression \(0.3^{\frac{4}
{5} }\cdot 0.3^{-\frac{3}
{10} }\)
and write the result using a root.
\(\sqrt{0.3}\)
\(\root{5}\of{0.3}\)
\(\root{10}\of{0.3^{7}}\)
\(\root{3}\of{0.3^8}\)
2010004807
Level:
B
Write the number \(\root{12}\of{5^{-4}}\)
as a power with a rational exponent.
\(5^{-\frac{1}
{3} }\)
\(5^{\frac{1}
{3} }\)
\(5^{3}\)
\(5^{-3}\)
2010004808
Level:
B
Assuming \(x\not \in \{-4;-1;0;4\}\),
simplify the following expression.
\[
\left(\frac{x+1}
{x^{2} +4x}\right)^{-1}\cdot \frac{x^{2} +x}
{x^2 - 16}
\]
\(\frac{x^2}
{x-4} \)
\(\frac{x^2}
{x+4} \)
\(\frac{2x}
{x-4} \)
\(\frac{x}
{x-4} \)
2010005701
Level:
B
The product of the numbers \( \left(\sqrt[6]{3}\cdot 81^{\frac14}\right)^{-1} \) and \( \sqrt[3]9\cdot \sqrt{3}\) equals:
\( 1 \)
\( \frac13 \)
\( \sqrt3 \)
\( 3 \)
2010005702
Level:
B
The number \(\sqrt[5]{(-3)^2}\cdot\left(\frac1{81}\right)^{-\frac25} \) equals:
\( 9 \)
\( -9 \)
\( 3 \)
\( -3 \)
2010005703
Level:
B
Calculate \( \left(4{.}3\cdot10^{-6}\right)\cdot\left(3\cdot10^{9}\right) \) and give the result in the scientific notation.
\( 12\,900 = 1{.}29\cdot10^4\)
\( 12\,900 = 12{.}9\cdot10^3\)
\( 12\,900 = 129\cdot10^2\)
\( 0.000\,000\,000\,000 \,001\,29= 1{.}29\cdot10^{-15}\)
2010005704
Level:
B
Writing the expression \( \frac{(0.25)^{-2}\cdot (x \colon y^2)^{-2} }{(2y)^4\cdot x^{-2}}\), \( x\neq0\), \( y\neq0 \) in a simplified form, we will get:
\( 1\)
\( y^{-8} \)
\( x^{-4} \)
\( \frac14 \)
2010005705
Level:
B
Writing the expression \( \frac{16\cdot \sqrt[4]{4}\cdot \sqrt[3]{\frac12}}{\sqrt{8}\cdot\sqrt[3]{2}\cdot 4\cdot \sqrt[6]{16}} \) in the form of a power of \( 2 \), we will get:
\( 2^{-\frac13} \)
\( 2^{\frac13} \)
\( 2^{-\frac23} \)
\( 2^{\frac56} \)
2010005706
Level:
B
What is the value of \( \left(3^{\sqrt6+\sqrt2}\right)^{\sqrt6-\sqrt2} \)?
\( 81\)
\( 3^{8} \)
\( 3^{\sqrt{32}} \)
\( 3^{2\sqrt{6}} \)