Question

Simplify
Please help as soon as possible ​

Answer 1

$\huge \mathcal\colorbox{lightblue}{Hey...}$

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$\mathcal{(( { \frac{13}{15} }^{3}) \times { (\frac{13}{15} }^{5} ))^{2} \div { (\frac{13}{15}) }^{9} } \\ = \mathcal( ({ \frac{13}{15} )}^{3 + 5} )^{2} \div { \frac{13}{15} }^{9} \\ = (\frac{13}{15} )^{8 \times 2} \div { \frac{13}{15} }^{9} \\ = { \frac{13}{15} }^{16 - 9} \\ = \mathcal \blue{ { \frac{13}{15} }^{7} }$

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Answer 2

Question :-

$\sf{\dfrac{{ \bigg[ \: \: \bigg({\dfrac{13}{15}}\bigg)^{3} \times { \bigg(\dfrac{13}{15} \bigg)}^{5} \: \: \bigg]}^{2}}{{\bigg( \dfrac{13}{15}} \bigg)^{9}}}$

Answer :-

$\bf{\dag} \: \: \:\frak{{\bigg(\dfrac{13}{15} \bigg)}^{7}}$

Step-by-step explanation:

To Find :-

The value of :-

$\sf{\dfrac{{ \bigg[ \: \: \bigg({\dfrac{13}{15}}\bigg)^{3} \times { \bigg(\dfrac{13}{15} \bigg)}^{5} \: \: \bigg]}^{2}}{{\bigg( \dfrac{13}{15}} \bigg)^{9}}}$

★ Solution

$\sf{ \longrightarrow \: \: \dfrac{{ \bigg[ \: \: \bigg({\dfrac{13}{15}}\bigg)^{3} \times { \bigg(\dfrac{13}{15} \bigg)}^{5} \: \: \bigg]}^{2}}{{\bigg( \dfrac{13}{15}} \bigg)^{9}}}$

By using the law of exponent [xᵐ × xⁿ = xᵐ⁺ⁿ], We get,

$\sf{ \longrightarrow \: \: \dfrac{{ \bigg[ \: \: \bigg({\dfrac{13}{15}}\bigg)^{(3 + 5)} \: \: \bigg]}^{2}}{{\bigg( \dfrac{13}{15}} \bigg)^{9}}}$

$\sf{ \longrightarrow \: \: \dfrac{{ \bigg[ \: \: \bigg({\dfrac{13}{15}}\bigg)^{8} \: \: \bigg]}^{2}}{{\bigg( \dfrac{13}{15}} \bigg)^{9}}}$

By using the law of exponent [{(xᵐ)ⁿ} = xᵐⁿ], We get,

$\sf{ \longrightarrow \: \: \dfrac{ \: \: \: \: \: \: \: { \bigg( \: \: {\dfrac{13}{15}} \: \: \bigg)}^{(8 \times 2)}}{{\bigg( \dfrac{13}{15}} \bigg)^{9}}}$

$\sf{ \longrightarrow \: \: \dfrac{ \: { \bigg({\dfrac{13}{15}} \bigg)}^{16}}{{\bigg( \dfrac{13}{15}} \bigg)^{9}}}$

By using the law of exponent [xᵐ/xⁿ = xᵐ⁻ⁿ], We get,

$\sf{ \longrightarrow \: \: {\bigg(\dfrac{13}{15} \bigg)}^{(16 - 9)}}$

$\sf{ \longrightarrow \: \: {\bigg(\dfrac{13}{15} \bigg)}^{7}}$

Hence,

$\sf{ \bigstar \: \: \dfrac{{ \bigg[ \: \: \bigg({\dfrac{13}{15}}\bigg)^{3} \times { \bigg(\dfrac{13}{15} \bigg)}^{5} \: \: \bigg]}^{2}}{{\bigg( \dfrac{13}{15}} \bigg)^{9}} = } \: \bf{\bigg(\dfrac{13}{15} \bigg)^{7}}$