Question

Please solve this now....

$\rm \: \large \bigg( \dfrac{ {x}^{p} }{ {x}^{q} } \bigg)^{p + q} \times \large \bigg( \dfrac{ {x}^{q} }{ {x}^{r} } \bigg)^{q + r} \times \large \bigg( \dfrac{ {x}^{r} }{ {x}^{p} } \bigg)^{ r + p}$
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Answer 1

Explanation :-

$\rm : \: \implies \large \bigg( \dfrac{ {x}^{p} }{ {x}^{q} } \bigg)^{p + q} \times \large \bigg( \dfrac{ {x}^{q} }{ {x}^{r} } \bigg)^{q + r} \times \large \bigg( \dfrac{ {x}^{r} }{ {x}^{p} } \bigg)^{ r + p}$

$\rm : \: \implies \large \bigg( { {x}^{p - q} } \bigg)^{p + q} \times \large \bigg( { {x}^{q - r} } \bigg)^{q + r} \times \large \bigg( { {x}^{r - p} }{ } \bigg)^{ r + p}$

$\rm : \: \implies \large \bigg( { {x} } \bigg)^{{(p - q)}(p + q)} \times \large \bigg( { {x}^{} } \bigg)^{(q - r)(q + r)} \times \large \bigg( { {x} }{ } \bigg)^{( r - p)(r + p)}$

$\rm : \: \implies \large \bigg( { {x} } \bigg)^{{( {p}^{2} - {q}^{2} )}} \times \large \bigg( { {x}^{} } \bigg)^{( {q}^{2} - {r}^{2} )} \times \large \bigg( { {x} }{ } \bigg)^{( {r}^{2} - {p}^{2} )}$

$\rm : \: \implies \large \bigg( { {x} } \bigg)^{{{( {p}^{2} - {q}^{2} )}} + {( {q}^{2} - {r}^{2} )} + {( {r}^{2} - {p}^{2} )}}$

$\rm : \: \implies \large \bigg( { {x} } \bigg)^{{{( {p}^{2} - {q}^{2} }} + { {q}^{2} - {r}^{2} } + { {r}^{2} - {p}^{2} )}}$

$\rm : \: \implies \large \bigg( { {x} } \bigg)^{{{( {p}^{2} - {p}^{2} + {q}^{2} }} - { {q}^{2} + {r}^{2} } - { {r}^{2} )}}$

$\rm : \: \implies \large \bigg( { {x} } \bigg)^{0} =1$

More to Know :-

$\begin{gathered}\boxed{\begin{array}{c}\bf{\dag}\:\:\underline{\text{Law of Exponents :}}\\\\\bigstar\:\:\sf\dfrac{a^m}{a^n} = a^{m - n}\\\\\bigstar\:\:\sf{(a^m)^n = a^{mn}}\\\\\bigstar\:\:\sf(a^m)(a^n) = a^{m + n}\\\\\bigstar\:\:\sf\dfrac{1}{a^n} = a^{-n}\\\\\bigstar\:\:\sf\sqrt[\sf n]{\sf a} = (a)^{\dfrac{1}{n}}\end {array}}\end{gathered}$