Question

7) Express as powers of rational number
$\frac{ - 125}{8}$
a)
$( \frac{ - 5}{3} ) {}^{3}$
b)
$( \frac{5}{2} ) {}^{3}$
c)
$( \frac{ - 5}{2} ) {}^{2}$
d)
$( \frac{2}{5} ) {}^{2}$
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Answer 1

Answer:

a)

${(\frac{-5}{3})}^{3} = \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \frac{( - 5)}{3} \times \frac{( - 5)}{3} \times \frac{( - 5)}{3} = \frac{( - 125)}{27}$

b)

${ (\frac{5}{2} )}^{3} \\ = \frac{5}{2} \times \frac{5}{2} \times \frac{5}{2} = \frac{125}{8}$

c)

${( \frac{ - 5}{2}) }^{2} \\ = \frac{( - 5)}{2} \times \frac{( - 5)}{2} = \frac{25}{4}$

d)

${ (\frac{2}{5}) }^{2} = \frac{2}{5} \times \frac{2}{5} = \frac{4}{25}$