Question

( 5^ -1 xy^ 2 5^ 2 xy^ -4 )^ 1 2 * ( 5^ -1 xy^ 3 5^ 3 x1^ -5 )^ -5/2​

Answer 1

Step-by-step Explanation :

${ \to \: \: \bf(5 ^ { -1 } xy ^ { 2 } 5 ^ { 2 } xy ^ { -4 } ) ^ { 1 } 2 \times (5 ^ { -1 } xy ^ { 3 } 5 ^ { 3 } x1 ^ { -5 } ) ^ { - \frac{ 5 }{ 2 } }}$

${ \to \: \: \tt\left(5^{1}xy^{2}xy^{-4}\right)^{1}\times 2\times \left(5^{-1}xy^{3}\times 5^{3}x\times 1^{-5}\right)^{-\frac{5}{2}} }$

$\tt{ \to \: \: \left(5^{1}x^{2}y^{2}y^{-4}\right)^{1}\times 2\times \left(5^{-1}xy^{3}\times 5^{3}x\times 1^{-5}\right)^{-\frac{5}{2}} }$

$\tt{ \to \: \: \left(5^{1}x^{2}y^{-2}\right)^{1}\times 2\times \left(5^{-1}xy^{3}\times 5^{3}x\times 1^{-5}\right)^{-\frac{5}{2}} }$

$\tt{ \to \: \: \left(5^{1}x^{2}y^{-2}\right)^{1}\times 2\times \left(5^{2}xy^{3}x\times 1^{-5}\right)^{-\frac{5}{2}} }$

$\tt{ \to \: \: \left(5^{1}x^{2}y^{-2}\right)^{1}\times 2\times \left(5^{2}x^{2}y^{3}\times 1^{-5}\right)^{-\frac{5}{2}} }$

${ \tt \to \: \: \left(5x^{2}y^{-2}\right)^{1}\times 2\times \left(5^{2}x^{2}y^{3}\times 1^{-5}\right)^{-\frac{5}{2}} }$

$\tt{ \to \: \:5x^{2}y^{-2}\times 2\times \left(5^{2}x^{2}y^{3}\times 1^{-5}\right)^{-\frac{5}{2}} }$

$\tt{ \to \: \: 10x^{2}y^{-2}\times \left(5^{2}x^{2}y^{3}\times 1^{-5}\right)^{-\frac{5}{2}} }$

$\tt{ \to \: \: 10x^{2}y^{-2}\times \left(25x^{2}y^{3}\times 1^{-5}\right)^{-\frac{5}{2}} }$

$\tt{ \to \: \: 10x^{2}y^{-2}\times \left(25x^{2}y^{3}\times 1\right)^{-\frac{5}{2}} }$

$\tt{ \to \: \: 10x^{2}y^{-2}\times \left(25x^{2}y^{3}\right)^{-\frac{5}{2}} }$

$\tt {\to \: \: 10x^{2}y^{-2}\times 25^{-\frac{5}{2}}\left(x^{2}\right)^{-\frac{5}{2}}\left(y^{3}\right)^{-\frac{5}{2}} }$

$\tt{ \to \: \: 10x^{2}y^{-2}\times 25^{-\frac{5}{2}}x^{-5}\left(y^{3}\right)^{-\frac{5}{2}} }$

$\tt{ \to \: \: 10x^{2}y^{-2}\times 25^{-\frac{5}{2}}x^{-5}y^{-\frac{15}{2}} }$

$\tt{ \to \: \: 10x^{2}y^{-2}\times \left(\frac{1}{3125}\right)x^{-5}y^{-\frac{15}{2}} }$

$\tt {\to \: \: \frac{2}{625}x^{2}y^{-2}x^{-5}y^{-\frac{15}{2}} }$

$\tt{ \to \: \: \frac{2}{625}x^{-3}y^{-2}y^{-\frac{15}{2}} }$

$\underline{ \boxed{\bf{ \to \: \: \frac{2}{625}x^{-3}y^{-\frac{19}{2}} }}} \: \: \bigstar$

.°. The equation is solved now !!