Question

ayudaa con esto plsssss se los agradezco

Answer 1

Explicación paso a paso:

a)

1ra manera:

$( \frac{2}{3} ) {}^{2} \div \frac{2}{3} = \frac{4}{9} \times \frac{3}{2} = \frac{2}{3}$

2da manera:

$( \frac{2}{3} ) {}^{2} \div \frac{2}{3} = \frac{ \frac{4}{9} }{ \frac{2}{3} } = \frac{12}{18} = \frac{2}{3}$

b)

1ra manera:

$( \frac{1}{2} \times \frac{1}{2} ) {}^{2} = ( \frac{1}{4} ) {}^{2} = \frac{1}{16}$

2da manera:

$( \frac{1}{2} \times \frac{1}{2} ) {}^{2} = ( \frac{1}{2} ) {}^{2} \times ( \frac{1}{2} ) {}^{2} = \frac{1}{4} \times \frac{1}{4} = \frac{1}{16}$

c)

1ra manera:

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

2da manera:

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

d)

1ra manera:

$( \frac{3}{2} + \frac{1}{3} ) {}^{2} = (\frac{11}{6} ) {}^{2} = \frac{121}{36}$

2da manera:

$( \frac{3}{2} + \frac{1}{3} ) {}^{2} = ( \frac{3}{2} ) {}^{2} + 2( \frac{3}{2} )( \frac{1}{3} ) + ( \frac{1}{3} ) {}^{2} = \frac{9}{4} + 1 + \frac{1}{9} = \frac{13}{4} + \frac{1}{9} = \frac{121}{36}$

e)

1ra manera:

$\sqrt{ \frac{4}{25} \times \frac{9}{36} } = \sqrt{ \frac{9}{225} } = \frac{ \sqrt{9} }{ \sqrt{225} } = \frac{3}{15} = \frac{1}{5}$

2da manera:

$\sqrt{ \frac{4}{25} \times \frac{9}{36} } = \sqrt{ \frac{4}{25} } \times \sqrt{ \frac{9}{36} } = \frac{ \sqrt{4} }{ \sqrt{25} } \times \frac{ \sqrt{9} }{ \sqrt{36} } = \frac{2}{5} \times \frac{3}{36} = \frac{1}{5}$

Disculpa, se me acabó el tiempo, pero espero haberte ayudado con los que hice :)