Expressions with exponents and radicals

1003118005

Level:

Determine the numbers

a

and

b

if you know that

(\sqrt{5} - 3) (a \sqrt{5} + b) = - 9 \sqrt{5} + 5 \sqrt{5}

a = 3, b = 5

a = \sqrt{5}, b = 3

a = - 3, b = 1

a = 5, b = \sqrt{5}

1003118009

Level:

The square of the number

\sqrt{2} - \sqrt[4]{2}

is equal to:

2 - 2 \sqrt[4]{8} + \sqrt{2}

2 - 2 \sqrt[4]{2} + \sqrt{2}

2 - 2 \sqrt[16]{8} + \sqrt[8]{2}

2 - \sqrt{2}

1003118103

Level:

Express

\frac{\sqrt[3]{5} \sqrt[6]{5}}{3 \cdot 25^{3} + 2 \cdot 125^{2}}

as a power of

5

5^{- \frac{13}{2}}

5^{- 5}

5^{- 6}

5^{- \frac{11}{2}}

1003118107

Level:

The number

{(\frac{27^{- 4} \cdot 8^{- 4}}{16^{- 2} \cdot 9^{- 5}})}^{- 3}

equals:

12^{6}

6^{6}

6^{12}

\frac{1}{3^{6} \cdot 2^{12}}

1003118603

Level:

Select the number that equals

\sqrt[5]{64}

2 \sqrt[5]{2}

\frac{\sqrt[5]{2}}{2}

\sqrt{2}

2

1003118605

Level:

\frac{2 \cdot \sqrt[3]{2}}{\sqrt{8}} = 2^{x}

, then

x = - \frac{1}{6}

x = 0

x = \frac{1}{3}

x = - 4

1003118607

Level:

Which of the following numbers are ordered from least to greatest?

(0.3)^{4}

0.027

(0.3)^{\sqrt{2}}

81^{\frac{3}{4}}

16^{\frac{1}{4}}

7^{- 2}

{(\frac{2}{3})}^{1.4}

{(\frac{2}{3})}^{π}

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

7^{0}

7^{- 1}

7^{- 2}

1003118608

Level:

Express the value of the expression

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

as a decimal number.

2.4

0.41 \overset{―}{6} \dots

\frac{12}{5}

- 1. \overset{―}{3}

1003124901

Level:

The fraction

\frac{1 + \sqrt{3}}{3 + \sqrt{11}}

is equal to:

\frac{\sqrt{11} - 3}{\sqrt{3} - 1}

9

\frac{\sqrt{11} - 3}{1 - \sqrt{3}}

\frac{\sqrt{11} + 2 \sqrt{3}}{2}

1003124907

Level:

The multiplicative inverse of the number

\frac{\sqrt[3]{27^{2}} : 9^{\frac{1}{2}}}{\sqrt[3]{9}}

is:

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

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

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

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

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Expressions with exponents and radicals

1003118005

1003118009

1003118103

1003118107

1003118603

1003118605

1003118607

1003118608

1003124901

1003124907

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