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By what number \(\frac{2^{-6}}{3}\) be divided that the quotient is equals to \(\frac{3^{-6}}{2}\)
1. \(\left(\frac{3}{2} \right)^5\)
2. \(\left(\frac{2}{3} \right)^6\)
3. \(\left(\frac{2}{3} \right)^{12}\)
4. \(\left(\frac{3}{2} \right)^{12}\)

1 Answer

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Best answer
Correct Answer - Option 1 : \(\left(\frac{3}{2} \right)^5\)

Concept:
We know that

Dividend ÷ Divisor = Quotient

Given:

Dividend = \(\frac{2^{-6}}{3}\)

Quotient = \(\frac{3^{-6}}{2}\)

Calculation:

The required number, Divisor = Dividend ÷ Quotient

⇒ \(\rm Divisor = \frac{{\frac{{{2^{ - 6}}}}{3}}}{{\frac{{{3^{ - 6}}}}{2}}}\)

⇒ \(Divisor = \frac{{{2^{ - 5}}}}{{{3^{ - 5}}}} = {\left( {\frac{3}{2}} \right)^5}\)

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