Expressions with exponents and radicals

1003032205

Level:

Order the numbers

a = {4.5}^{- 2}

b = {\sqrt{0.4}}^{\sqrt{12}}

c = {2.5}^{- 2.4}

d = 0.064

from the smallest to the largest.

a < d < c < b

d < a < c < b

a < d < b < c

c < a < b < d

1003032206

Level:

Simplifying the expression

\frac{{(\frac{1}{3})}^{- 3} \cdot 27^{- 2}}{9^{- 5} \cdot \sqrt{3^{4}}}

we will get:

3^{5}

3^{- 11}

3^{2}

3^{- 5}

1003032207

Level:

Let

x = 2^{4 \sqrt{2}}

y = 4^{\frac{\sqrt{2}}{2}}

and

z = 8^{- \frac{\sqrt{2}}{3}}

. Which two numbers are multiplicative inverses of each other?

y

z

x

y

x

z

no two numbers

1003032208

Level:

Write the number

\frac{1}{3} \cdot 9^{π + \frac{1}{2}} : 81^{2 π}

in the form of

a^{x}

, where

a

is a natural number.

3^{- 6 π}

3^{6 π}

3^{- \frac{1}{2} + 3 π}

9^{- \frac{1}{2} + 3 π}

1003032209

Level:

What is the value of

{(2^{\sqrt{7} - \sqrt{2}})}^{\sqrt{7} + \sqrt{2}}

32

2^{\sqrt{45}}

2^{9}

1024

1003032210

Level:

Which of the given numbers belongs to the interval

(- 5; 5)

3 {(\sqrt{0.1})}^{4} \cdot {(\sqrt{3})}^{8}

{(3 \sqrt{5})}^{2} - {(\sqrt{2})}^{6}

{(\sqrt{3})}^{4} - {(\sqrt{2})}^{4}

3 {(\sqrt{0.1})}^{4} + {(\sqrt{3})}^{8}

1003034107

Level:

By computing

4^{11} \cdot 4^{- 11}

we get:

1

0

4^{22}

16^{- 121}

1003099408

Level:

The value of the expression

\frac{1}{2} \cdot [\frac{5 \cdot {(0.2 + \frac{3}{5})}^{2}}{3.2}] + \frac{1}{3}

is:

\frac{5}{6}

\frac{3}{2}

\frac{4}{3}

\frac{5}{2}

1003099409

Level:

Simplifying

{(\frac{1}{{(\sqrt[3]{729} + \sqrt[4]{256} + 2)}^{0}})}^{- 2}

we get:

1

\frac{1}{15}

\frac{1}{225}

15

1003099410

Level:

The value of the multiplicative inverse of

{[2^{- 2} + {(\frac{1}{6})}^{- 1}]}^{\frac{1}{2}}

is:

\frac{2}{5}

\frac{1}{2} + \sqrt{6}

\frac{4}{25}

\frac{5}{2}

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Expressions with exponents and radicals

1003032205

1003032206

1003032207

1003032208

1003032209

1003032210

1003034107

1003099408

1003099409

1003099410

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