9000013503
Level:
B
Write the number \(\root{6}\of{3^{-3}}\)
as a power with a rational exponent.
\(3^{-\frac{1}
{2} }\)
\(3^{\frac{1}
{2} }\)
\(3^{2}\)
\(3^{-2}\)
B
9000010602
Level:
B
Identify a function which has a domain
\((-\infty ;-2)\cup (2;\infty )\).
\(y = \sqrt{ \frac{1}
{x^{2}-4}}\)
\(y = \frac{1}
{x^{2}-4}\)
\(y = \sqrt{x^{2 } + 4}\)
\(y = \sqrt{x^{2 } - 2}\)
\(y = \sqrt{x^{2 } - 4}\)
\(y = \sqrt{ \frac{1}
{x^{2}-2}}\)
9000014201
Level:
B
Find intersection points of the graph of the rational function
\(
f(x) = \frac{2x - 3}
{x - 2}
\)
with \(y\)-axis.
\(Y = \left [0; \frac{3}
{2}\right ]\)
\(Y = \left [\frac{3}
{2};0\right ]\)
\(Y _{1} = \left [0; \frac{3}
{2}\right ]\text{ and }Y _{2} = \left [\frac{3}
{2};0\right ]\)
\(Y = \left [2;2\right ]\)
9000014202
Level:
B
Find the intersections of the graph of the rational function
\(f(x) = \frac{x+2}
{2-x}\) with
\(x\)-axis.
\(X = \left [-2;0\right ]\)
\(X = \left [0;-2\right ]\)
\(X_{1} = \left [0;-2\right ]\text{ and }X_{2} = \left [-2;0\right ]\)
\(X = \left [2;0\right ]\)
9000010503
Level:
B
For \(x\in \mathbb{R}\),
\(x > 0\),
simplify the following expression.
\[
\root{5}\of{x}\cdot \root{}\of{x}
\]
\(\root{10}\of{x^{7}}\)
\(\root{10}\of{x}\)
\(\root{5}\of{x^{2}}\)
\(\root{10}\of{x^{2}}\)
9000013502
Level:
B
Simplify the expression \(0.5^{\frac{6}
{7} }\cdot 0.5^{-\frac{5}
{14} }\)
and write the result using a root.
\(\sqrt{0.5}\)
\(\root{7}\of{0.5}\)
\(\root{14}\of{0.5^{11}}\)
\(\root{14}\of{0.5}\)
9000010506
Level:
B
For \(x\in \mathbb{R}\),
\(x > 0\),
simplify the following expression.
\[
x\cdot \root{}\of{x}\cdot \root{3}\of{x}
\]
\(x\root{6}\of{x^{5}}\)
\(\root{6}\of{x^{3}}\)
\(\root{}\of{x}\)
\(x^{5}\root{6}\of{x^{5}}\)
9000010510
Level:
B
For \(x\in \mathbb{R}\),
\(x > 0\),
simplify the following expression.
\[
\root{3}\of{x} : \root{6}\of{x}
\]
\(\root{6}\of{x}\)
\(\root{}\of{x}\)
\(\root{3}\of{x^{2}}\)
\(x\)
9000013501
Level:
B
Write the expression \(2^{\frac{3}
{4} }\)
in an equivalent form which does not contain a rational exponent.
\(\root{4}\of{2^{3}}\)
\(\root{4}\of{2}\)
\(\root{3}\of{2^{4}}\)
\(\root{4}\of{3^{2}}\)
9000013504
Level:
B
Simplify \(\sqrt{\root{4}\of{25}}\).
\(\root{4}\of{5}\)
\(\root{8}\of{5}\)
\(\root{4}\of{25}\)
\(\sqrt{5}\)