Question

By what number should ((-3)/5)^(-3)be divided so that the quotient may be (6/125)^(-2)?

Answer 1

Step-by-step explanation:

We know that

$dividend = </p><p>divisor \times quotient + reminder$

$here \: dividend \: = ({ \frac{ - 3}{5} })^{ - 3}$

$quotient \: = ( { \frac{6}{125} })^{ - 2}$

then,

According to above formula,

$({ \frac{ - 3}{5} })^{ - 3} = divisor \times ({ \frac{6}{125} })^{ - 2} + 0$

$we \: use \: this \: formula \: \\ ( { \frac{a}{b} })^{ - n} = ({ \frac{b}{a} })^{n}$

Now ,

$({ \frac{ - 5}{3} })^{3} = \: divisor \: \times \: ({ \frac{125}{6} })^{2}$

$\frac{( { \frac{ - 5}{3} })^{3} }{ ({ \frac{125}{6} })^{2} } = divisor$

$we \: use \: this \: formula \: \frac{ \frac{a}{b} }{ \frac{c}{d} } \: = \: \frac{a}{b} \times \frac{c}{d}$

So,

$({ \frac{ - 5}{3} })^{3} \times ({ \frac{6}{125} })^{2} = divisor$

Hence,

$divisor = - \frac{5}{3} \times \frac{5}{3} \times \frac{5}{3} \times \frac{6}{125} \times \frac{6}{125}$

$divisor = - \frac{1}{3} \times 2 \times \frac{2}{125}$

$divisor = - \frac{4}{375} \: answer$