Question

( If 9 1⁄3 × 3 2⁄3 ) / (27 1⁄2 × 3 1⁄6) and Simplify 0.34 - 0.0032 and express the result in the form p/q, where p & q are integers and q ≠ 0. (both are different questions)

Answer 1

Solution

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${ \: \: \: \: \: \implies \sf \dfrac{ {9}^{ \frac{1}{3} } \times {3}^{ \frac{2}{3} } }{ {27}^{ \frac{1}{2} } \times {3}^{ \frac{1}{6} } } }$

${ \: \: \: \: \: \implies \sf \dfrac{ {3}^{ \frac{2}{3} } \times {3}^{ \frac{2}{3} } }{ {3}^{ \frac{3}{2} } \times {3}^{ \frac{1}{6} } } }$

${ \: \: \: \: \: \implies \sf \dfrac{ {3}^{ \frac{2}{3} + \frac{2}{3} } }{ {3}^{ \frac{3}{2} + \frac{1}{6} } } }$

${ \: \: \: \: \: \implies \sf \dfrac{ {3}^{ \frac{2 + 2}{3} } }{ {3}^{ \frac{9 + 1}{6} } } }$

${ \: \: \: \: \: \implies \sf \dfrac{ {3}^{ \frac{4}{3} } }{ {3}^{ \frac{10}{6} } } }$

${ \: \: \: \: \: \implies \sf {3}^{ \frac{4}{3} - \frac{10}{6} } }$

${ \: \: \: \: \: \implies \sf {3}^{ \frac{8 - 10}{6} } }$

${ \: \: \: \: \: \implies \sf {3}^{ \frac{ - 2}{6} } }$

${ \: \: \: \: \: \implies \sf {3}^{ \frac{ - 1}{3} } }$

${ \: \: \: \: \: \implies \sf \dfrac{1}{ {3}^{ \frac{1}{3} } } }$

$\boxed {\pink{ \: \: \: \: \: \implies \sf \dfrac{ {9}^{ \frac{1}{3} } \times {3}^{ \frac{2}{3} } }{ {27}^{ \frac{1}{2} } \times {3}^{ \frac{1}{6} } } = \dfrac{1}{ {3}^{ \frac{1}{3} }} }}$

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Simplify 0.34 - 0.0032

$\sf \: \: \: \: \: \: \: \: \: \: \implies0.34 -0.0032$

$\sf \: \: \: \: \: \: \: \: \: \: \implies0.3368$

$\sf \: \: \: \: \: \: \: \: \: \: \implies \dfrac{ 3368}{10000}$

$\sf \: \: \: \: \: \: \: \: \: \: \implies \dfrac{1684}{5000}$

$\sf \: \: \: \: \: \: \: \: \: \: \implies \dfrac{824}{2500}$

$\sf \: \: \: \: \: \: \: \: \: \: \implies \dfrac{421}{1250}$

$\boxed{ \pink{ \sf 0.34 -0.0032 = \dfrac{421}{1250} }}$