9000010503
Level:
B
For \(x\in \mathbb{R}\),
\(x > 0\),
simplify the following expression.
\[
\root{5}\of{x}\cdot \root{}\of{x}
\]
\(\root{10}\of{x^{7}}\)
\(\root{10}\of{x}\)
\(\root{5}\of{x^{2}}\)
\(\root{10}\of{x^{2}}\)
B
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 \(\sqrt{\root{4}\of{25}}\).
\(\root{4}\of{5}\)
\(\root{8}\of{5}\)
\(\root{4}\of{25}\)
\(\sqrt{5}\)
9000013507
Level:
B
Simplify \(\root{4}\of{16\cdot 81}\).
\(6\)
\(36\)
\(\sqrt{6}\)
\(\root{4}\of{6}\)
9000010601
Level:
B
Identify a function which has a domain
\([ - 3;1] \).
\(y = \sqrt{-x^{2 } - 2x + 3}\)
\(y = \sqrt{-x^{2 } + 2x - 3}\)
\(y = \sqrt{x^{2 } + 2x - 3}\)
\(y = \sqrt{x^{2 } - 2x + 3}\)
\(y = \sqrt{\frac{x+3}
{x+1}}\)
\(y = \sqrt{\frac{x-1}
{x+3}}\)
9000010603
Level:
B
Identify a function which has a domain
\(\left (-\infty ;-\frac{3}
{2}\right ] \).
\(y = \sqrt{-2x - 3}\)
\(y = \sqrt{3x + 2}\)
\(y = -\sqrt{2 - 3x}\)
\(y = \sqrt{x + \frac{3}
{2}}\)
\(y = \sqrt{x^{2 } - 3x}\)
\(y = \frac{1}
{3x+2}\)
9000010604
Level:
B
Identify a function which has a domain
\([ - 3;5)\).
\(y = \sqrt{\frac{x+3}
{5-x}}\)
\(y = \sqrt{(x - 3)(x + 5)}\)
\(y = \sqrt{\frac{x-5}
{x+3}}\)
\(y = \sqrt{(x - 5)(x + 3)}\)
\(y =\log \frac{x+5}
{x-3}\)
\(y =\log \frac{x+3}
{x-5}\)