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liraira [26]
2 years ago
10

(27/8)^1/3×[243/32)^1/5÷(2/3)^2]Simplify this question sir pleasehelpme​

Mathematics
2 answers:
gtnhenbr [62]2 years ago
6 0

Step-by-step explanation:

=  {( \frac{27}{8} )}^{ \frac{1}{3} }  \times ( \frac{243}{32} )^{ \frac{1}{5} }  \div  {( \frac{2}{3} )}^{2}

=  { ({ (\frac{3}{2} )}^{3}) }^{ \frac{1}{3} }  \times  {( {( \frac{3}{2}) }^{5} )}^{ \frac{1}{5} }  \div  {( \frac{2}{3} )}^{2}

=  {( \frac{3}{2} )}^{3 \times  \frac{1}{3} }  \times  {( \frac{3}{2} )}^{5 \times  \frac{1}{5} }  \times  {( \frac{3}{2} )}^{2}

=  \frac{3}{2}  \times  \frac{3}{2}  \times  {( \frac{3}{2} )}^{2}

=  {( \frac{3}{2} )}^{1 + 1 + 2}

=  {( \frac{3}{2} )}^{4} \:  or \:  \frac{81}{16}

Usimov [2.4K]2 years ago
3 0

\large\underline{\sf{Solution-}}

\sf{\longmapsto{\bigg( \dfrac{27}{8} \bigg)^{\frac{1}{3}} \times \Bigg[\bigg( \dfrac{243}{32} \bigg)^{\frac{1}{5}} \div \bigg(\dfrac{2}{3} \bigg)^{2}\Bigg]}} \\

We can write as :

27 = 3 × 3 × 3 = 3³

8 = 2 × 2 × 2 = 2³

243 = 3 × 3 × 3 × 3 × 3 = 3⁵

32 = 2 × 2 × 2 ×2 × 2 = 2⁵

\sf{\longmapsto{\bigg( \dfrac{3 \times 3 \times 3}{2 \times 2 \times 2} \bigg)^{\frac{1}{3}} \times \Bigg[\bigg( \dfrac{3 \times 3 \times 3 \times 3 \times 3}{2 \times 2 \times 2 \times 2 \times 2} \bigg)^{\frac{1}{5}} \div \bigg(\dfrac{2}{3} \bigg)^{2}\Bigg]}} \\

\sf{\longmapsto{\bigg( \dfrac{{(3)}^{3}}{{(2)}^{3}} \bigg)^{\frac{1}{3}} \times \Bigg[\bigg( \dfrac{({3}^{5})}{{(2)}^{5}} \bigg)^{\frac{1}{5}} \div \bigg(\dfrac{2}{3} \bigg)^{2}\Bigg]}} \\

Now, we can write as :

(3³/2³) = (3/2)³

(3⁵/2⁵) = (3/2)⁵

\sf{\longmapsto{\left\{\bigg(\frac{3}{2} \bigg)^{3}  \right\}^{\frac{1}{3}} \times \Bigg[\left\{\bigg(\frac{3}{2} \bigg)^{5} \right\}^{\frac{1}{5}} \div \bigg(\dfrac{2}{3} \bigg)^{2}\Bigg]}} \\

Now using law of exponent :

{\sf{({a}^{m})^{n} = {a}^{mn}}}

\sf{\longmapsto{\bigg( \frac{3}{2} \bigg)^{3 \times \frac{1}{3}} \times \Bigg[\bigg(\frac{3}{2}  \bigg)^{5 \times \frac{1}{5}} \div \bigg(\dfrac{2}{3} \bigg)^{2}\Bigg]}} \\

\sf{\longmapsto{\bigg( \frac{3}{2} \bigg)^{\frac{3}{3}} \times \Bigg[\bigg(\frac{3}{2}  \bigg)^{\frac{5}{5}} \div \bigg(\dfrac{2}{3} \bigg)^{2}\Bigg]}} \\

\sf{\longmapsto{\bigg( \frac{3}{2} \bigg)^{1} \times\Bigg[\bigg(\frac{3}{2}  \bigg)^{1} \div \bigg(\dfrac{2}{3} \bigg)^{2}\Bigg]}} \\

\sf{\longmapsto{\bigg( \frac{3}{2} \bigg)^{1} \times \Bigg[\bigg(\frac{3}{2}  \bigg)^{1} \times  \bigg(\dfrac{3}{2} \bigg)^{2}\Bigg]}} \\

\sf{\longmapsto{\bigg( \frac{3}{2} \bigg)^{1} \times \Bigg[\bigg(\frac{3}{2}  \bigg)^{1} \times  \bigg(\dfrac{3}{2} \times  \dfrac{3}{2} \bigg)\Bigg]}} \\

\sf{\longmapsto{\bigg( \dfrac{3}{2} \bigg)^{1} \times \Bigg[\bigg(\dfrac{3}{2}  \bigg)^{1} \times  \bigg(\dfrac{3 \times 3}{2 \times 2}\bigg)\Bigg]}} \\

\sf{\longmapsto{\bigg( \dfrac{3}{2} \bigg)^{1} \times \Bigg[\bigg(\dfrac{3}{2}  \bigg)^{1} \times  \bigg(\dfrac{9}{4}\bigg)\Bigg]}} \\

\sf{\longmapsto{\bigg( \frac{3}{2} \bigg)\times \Bigg[\bigg(\frac{3}{2}  \bigg)\times  \bigg(\dfrac{9}{4}\bigg)\Bigg]}} \\

\sf{\longmapsto{\bigg( \dfrac{3}{2} \bigg)\times \Bigg[ \:  \: \dfrac{3}{2}   \times \dfrac{9}{4} \:  \: \Bigg]}}\\

\sf{\longmapsto{\bigg( \dfrac{3}{2} \bigg)\times \Bigg[ \:  \: \dfrac{3 \times 9}{2 \times 4} \:  \: \Bigg]}} \\

\sf{\longmapsto{\bigg(\dfrac{3}{2} \bigg)\times \Bigg[ \:  \: \dfrac{27}{8} \:  \: \Bigg]}} \\

\sf{\longmapsto{\dfrac{3}{2} \times \dfrac{27}{8}}} \\

\sf{\longmapsto{\dfrac{3 \times 27}{2 \times 8}}} \\

\sf{\longmapsto{\dfrac{81}{16}}\: ≈ \:5.0625\:\red{Ans.}} \\

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