Expressions with exponents and radicals

1003032103

Level:

The number

\sqrt[3]{{(- 27)}^{- 1}} \cdot 81^{\frac{3}{4}}

equals:

- 9

- 27

3

9

1003032104

Level:

The number

\sqrt[3]{(- 2)^{4}} \cdot {(\frac{1}{16})}^{- \frac{2}{3}}

equals:

16

- 16

- 4

4

1003032105

Level:

Let

a = 5^{- 1} \cdot \sqrt{5}

b = 5^{- \frac{3}{2}} \cdot 25

c = 125^{\frac{1}{4}} : 5^{- 3}

d = 5^{\frac{1}{3}} \cdot 25^{- \frac{1}{3}}

. Which of these numbers is the biggest?

c

a

b

d

1003032106

Level:

The value of the expression

\frac{16^{\frac{3}{2}} - 16^{\frac{5}{4}}}{40}

is:

0.8

0.4

\frac{1}{20}

\frac{1}{40}

1003032108

Level:

Write the number

4^{- 5} \cdot 8^{2}

2^{m}

, where

m

is an integer.

2^{- 4}

2^{- 3}

2^{- 16}

2^{- 30}

1003032109

Level:

Calculate

(3.4 \cdot 10^{7}) \cdot (4 \cdot 10^{- 5})

and give the result in the scientific notation.

1 360 = 1.36 \cdot 10^{3}

1 360 = 13.6 \cdot 10^{2}

1 360 = 136 \cdot 10^{1}

1 360 000 000 000 = 1.36 \cdot 10^{12}

1003032201

Level:

Let

a = {(\frac{2}{3})}^{\sqrt{7} - \sqrt{3}}

and

b = {(\frac{2}{3})}^{\sqrt{3} + 2}

. Which of the following relations is true for

a

and

b

a > b

b > a

a = b

a \cdot b = {(\frac{2}{3})}^{2 \sqrt{7}}

1003032202

Level:

Writing the expression

\frac{(4 x)^{2} \cdot (x : y)^{- 2}}{(0.5)^{- 4} \cdot y^{- 1}}

x \neq 0

y \neq 0

in a simplified form, we will get:

y^{3}

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

8 y^{3}

256 y^{- 1}

1003032203

Level:

Writing the expression

\frac{\sqrt[3]{3} \cdot 9 \cdot \sqrt{27} \cdot \sqrt[6]{81}}{81 \cdot \sqrt[3]{\frac{1}{3}} \cdot \sqrt[4]{9}}

in the form of a power of

3

, we will get:

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

3^{- \frac{5}{6}}

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

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

1003032204

Level:

Order the numbers

a = 5^{\sqrt{5}}

b = 25 \sqrt{5}

c = 125^{\frac{4}{5}}

d = 25^{1.1}

from the smallest to the largest.

d < a < c < b

a < b < c < d

d < a < b < c

a < b < d < c

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Expressions with exponents and radicals

1003032103

1003032104

1003032105

1003032106

1003032108

1003032109

1003032201

1003032202

1003032203

1003032204

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