Question

DAU 55 PUNCTE ŞI COROANĂ.

Rezolvați:

(-2)³ = ?

.

$( - \frac {2}{3} ) {}^{2} =$ ?

$( - \frac{2}{3} ) {}^{3} =$ ?

$( \frac{4}{6} ) {}^{ - 2} =$ ?

$( \frac{5}{6} ) {}^{ - 3} =$ ?

$( - \frac{2}{4} ) {}^{ - 2}$ = ?

$( - \frac{2}{4} ) {}^{ - 3}$ = ?

Answer 1

$a) \\ \\ {( - 2)}^{3} = - {2}^{3} = - 8$

$b) \\ \\ {( - \frac{2}{3}) }^{2} = {( \frac{2}{3}) }^{2} = \frac{ {2}^{2} }{ {3}^{2} } = \frac{4}{9}$

$c) \\ \\ {( - \frac{2}{3}) }^{3} = - {( \frac{2}{3}) }^{3} = - \frac{ {2}^{3} }{ {3}^{3} } = - \frac{8}{27}$

$d) \\ \\ {( \frac{4}{6}) }^{ - 2} = {( \frac{2}{3}) }^{ - 2} = \frac{1}{ {( \frac{2}{3}) }^{2} } = \frac{1}{ \frac{ {2}^{2} }{ {3}^{2} } } = \frac{1}{ \frac{4}{9} } = \frac{9}{4}$

$e) \\ \\ {( \frac{5}{6}) }^{ - 3} = \frac{1}{ {( \frac{5}{6}) }^{3} } = \frac{1}{ \frac{ {5}^{3} }{ {6}^{3} } } = \frac{1}{ \frac{125}{216} } = \frac{216}{125}$

$f) \\ \\ {( \frac{2}{4}) }^{ - 2} = {( \frac{1}{2}) }^{ - 2} = \frac{1}{ {( \frac{1}{2}) }^{2} } = \frac{1}{ \frac{1}{ {2}^{2} } } = \frac{1}{ \frac{1}{4} } = 4$

$g) \\ \\ {( - \frac{2}{4}) }^{ - 3} = {( - \frac{1}{2}) }^{ - 3} = \frac{1}{( - \frac{1}{2}) ^{3} } = \frac{1}{ - {( \frac{1}{2}) }^{3} } = \frac{1}{ - \frac{1}{ {2}^{3} } } = \frac{1}{ - \frac{1}{8} } = - \frac{1}{ \frac{1}{8} } = - 8$

Answer 2

( - 2 )³ = - 8

( - 2 / 3 ) ² = + 2² / 3² = 4 / 9

( - 2 / 3 )³ = - 2³ / 3³ = - 8 / 27

( 4 / 6 ) ⁻ 2 = 1 / ( 4 / 6 )² = ( 6/ 4 )² = ( 3 / 2) ² = 3² / 2²= 9 / 4

( 5 / 6 ) ⁻ ³ = 1 / ( 5 / 6 )³ = 6³ / 5³ = 216 / 125 = 1,728

( - 2 / 4 )⁻² = ( - 1 / 2) ⁻² = 1 / ( - 1 / 2)² = + 2²/ 1² = 4

( - 2 / 4) ⁻³ = ( - 1 / 2 ) ⁻ ³ = 1 / ( - 1 / 2 )³ = - 2³ / 1³= - 8