Question

Simplify
Class 8 Exponents and powers ​

Answer 1

Simplifying :

• (Take this L.H.S)

$\\ \large \rm \: \leadsto \: \: \dfrac{( {3}^{5} {)}^{2} \times {5}^{3} }{ {9}^{2} \times 5 }$

Solving :

• Power ki power = power multiply

$\\ \large \sf \implies \: \frac{ {3}^{10} \times {5 }^{3} }{ {9}^{2} \times 5} \\ \\ \large \sf \: \implies \: \frac{59049 \times 125}{81 \times 5} \\ \\ \\ \large \sf \implies \: \frac{7381125}{405} \\ \\ \\ \large \sf \underline{ \boxed{ \sf \: = 18225}} \: l.h.s$

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Solving by identities :

• (take it as R.H.S)

☞︎︎︎ In division, When the basis are same then the powers are subtracted.

$\\ \large \rm \: \leadsto \: \: \dfrac{( {3}^{5} {)}^{2} \times {5}^{3} }{ {9}^{2} \times 5 }$

Here,

• 9² = (3²)²

$\\ \large \sf \implies \: \frac{( {3}^{5} {) }^{2} \times {5}^{3} }{( {3}^{2} {)}^{2} \times 5 } \\ \\ \\ \large \sf \implies \: \frac{{3}^{10} \times {5}^{3} }{{3}^{4} \times 5 } \\ \\ \\ \large \sf \: \implies \: ({3}^{10} \div {3}^{4} ) \times ( {5}^{3} \div {5}^{1} ) \\ \\ \large \sf \implies \: {3}^{10 - 4} \times {5}^{3 - 1} \\ \\ \large \sf \implies \: {3}^{6} \times {5}^{2} \\ \\ \large \sf \implies \: 729 \times 25 \\ \\ \large \sf \underline{ \boxed{ \sf \: = 18225 }} \: r.h.s$

R.H.S = L.H.S

• Hence Proved

Answer 2

Please check the attachment!
Hope it helps
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