Expressions with exponents and radicals

2010004804

Level:

For

x \in R

x > 0

, simplify the following expression.

\sqrt[3]{x} \cdot \sqrt[5]{x^{3}}

\sqrt[15]{x^{14}}

\sqrt[5]{x}

\sqrt[15]{x^{4}}

\sqrt{x}

2010004806

Level:

Simplify the expression

{0.3}^{\frac{4}{5}} \cdot {0.3}^{- \frac{3}{10}}

and write the result using a root.

\sqrt{0.3}

\sqrt[5]{0.3}

\sqrt[10]{{0.3}^{7}}

\sqrt[3]{{0.3}^{8}}

2010004807

Level:

Write the number

\sqrt[12]{5^{- 4}}

as a power with a rational exponent.

5^{- \frac{1}{3}}

5^{\frac{1}{3}}

5^{3}

5^{- 3}

2010004808

Level:

Assuming

x \notin {- 4; - 1; 0; 4}

, simplify the following expression.

{(\frac{x + 1}{x^{2} + 4 x})}^{- 1} \cdot \frac{x^{2} + x}{x^{2} - 16}

\frac{x^{2}}{x - 4}

\frac{x^{2}}{x + 4}

\frac{2 x}{x - 4}

\frac{x}{x - 4}

2010005701

Level:

The product of the numbers

{(\sqrt[6]{3} \cdot 81^{\frac{1}{4}})}^{- 1}

and

\sqrt[3]{9} \cdot \sqrt{3}

equals:

1

\frac{1}{3}

\sqrt{3}

3

2010005702

Level:

The number

\sqrt[5]{(- 3)^{2}} \cdot {(\frac{1}{81})}^{- \frac{2}{5}}

equals:

9

- 9

3

- 3

2010005703

Level:

Calculate

(4.3 \cdot 10^{- 6}) \cdot (3 \cdot 10^{9})

and give the result in the scientific notation.

12 900 = 1.29 \cdot 10^{4}

12 900 = 12.9 \cdot 10^{3}

12 900 = 129 \cdot 10^{2}

0.000 000 000 000 001 29 = 1.29 \cdot 10^{- 15}

2010005704

Level:

Writing the expression

\frac{(0.25)^{- 2} \cdot (x : y^{2})^{- 2}}{(2 y)^{4} \cdot x^{- 2}}

x \neq 0

y \neq 0

in a simplified form, we will get:

1

y^{- 8}

x^{- 4}

\frac{1}{4}

2010005705

Level:

Writing the expression

\frac{16 \cdot \sqrt[4]{4} \cdot \sqrt[3]{\frac{1}{2}}}{\sqrt{8} \cdot \sqrt[3]{2} \cdot 4 \cdot \sqrt[6]{16}}

in the form of a power of

2

, we will get:

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

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

2^{- \frac{2}{3}}

2^{\frac{5}{6}}

2010005706

Level:

What is the value of

{(3^{\sqrt{6} + \sqrt{2}})}^{\sqrt{6} - \sqrt{2}}

81

3^{8}

3^{\sqrt{32}}

3^{2 \sqrt{6}}

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Expressions with exponents and radicals

2010004804

2010004806

2010004807

2010004808

2010005701

2010005702

2010005703

2010005704

2010005705

2010005706

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