Expressions with powers and roots

2010005707

Level:

Which of the given numbers belongs to the interval \( [ -5;5 ]\)?

\( \left(\sqrt2\right)^4-\left(\sqrt3\right)^4 \)

\( 2\left(\sqrt{0{.}1}\right)^2\cdot\left(\sqrt2\right)^{10} \)

\( \left(2\sqrt{5}\right)^2-\left(\sqrt3\right)^6 \)

\( 2\left(\sqrt{0{.}1}\right)^4+\left(\sqrt2\right)^8 \)

9000010503

Level:

For \(x\in \mathbb{R}\), \(x > 0\), simplify the following expression. \[ \root{5}\of{x}\cdot \root{}\of{x} \]

\(\root{10}\of{x^{7}}\)

\(\root{10}\of{x}\)

\(\root{5}\of{x^{2}}\)

\(\root{10}\of{x^{2}}\)

9000010505

Level:

For \(x\in \mathbb{R}\), \(x > 0\), simplify the following expression. \[ \root{5}\of{x^{3}} : \root{3}\of{x} \]

\(\root{15}\of{x^{4}}\)

\(\root{5}\of{x}\)

\(\root{3}\of{x^{2}}\)

\(\root{5}\of{x^{2}}\)

9000010506

Level:

For \(x\in \mathbb{R}\), \(x > 0\), simplify the following expression. \[ x\cdot \root{}\of{x}\cdot \root{3}\of{x} \]

\(x\root{6}\of{x^{5}}\)

\(\root{6}\of{x^{3}}\)

\(\root{}\of{x}\)

\(x^{5}\root{6}\of{x^{5}}\)

9000010508

Level:

For \(x\in \mathbb{R}\), \(x > 0\), simplify the following expression. \[ \root{3}\of{x^{2}}\cdot \root{5}\of{x^{4}} \]

\(\root{15}\of{x^{22}}\)

\(\root{15}\of{x^{6}}\)

\(\root{15}\of{x^{8}}\)

\(x^{3}\root{15}\of{x}\)

9000010510

Level:

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:

Write the expression \(2^{\frac{3} {4} }\) in an equivalent form which does not contain a rational exponent.

\(\root{4}\of{2^{3}}\)

\(\root{4}\of{2}\)

\(\root{3}\of{2^{4}}\)

\(\root{4}\of{3^{2}}\)

9000013502

Level:

Simplify the expression \(0.5^{\frac{6} {7} }\cdot 0.5^{-\frac{5} {14} }\) and write the result using a root.

\(\sqrt{0.5}\)

\(\root{7}\of{0.5}\)

\(\root{14}\of{0.5^{11}}\)

\(\root{14}\of{0.5}\)

9000013503

Level:

Write the number \(\root{6}\of{3^{-3}}\) as a power with a rational exponent.

\(3^{-\frac{1} {2} }\)

\(3^{\frac{1} {2} }\)

\(3^{2}\)

\(3^{-2}\)

9000013504

Level:

Simplify \(\sqrt{\root{4}\of{25}}\).

\(\root{4}\of{5}\)

\(\root{8}\of{5}\)

\(\root{4}\of{25}\)

\(\sqrt{5}\)

Expressions with powers and roots

2010005707

9000010503

9000010505

9000010506

9000010508

9000010510

9000013501

9000013502

9000013503

9000013504

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