Question

simplify




pls give answer


answer will be -⁵/³​

Answer 1

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

Given that

$\rm :\longmapsto\:\dfrac{ {5}^{x + 2} - 6 \times {5}^{x + 1} }{13 \times {5}^{x} - 2 \times {5}^{x + 1} }$

We know,

$\boxed{ \sf \: {a}^{m + n} = {a}^{m} \times {a}^{n}}$

So, using this identity, we get

$\rm \:  =  \:  \: \dfrac{ {5}^{x} \times 5 \times 5 - 6 \times {5}^{x} \times 5}{13 \times {5}^{x} - 2 \times {5}^{x} \times 5 }$

$\rm \:  =  \:  \: \dfrac{ \red{{5}^{x} \times 5} \times 5 - 6 \times \red{{5}^{x} \times 5}}{13 \times \blue{{5}^{x}} - 2 \times \blue{ {5}^{x}} \times 5 }$

Now, take common from numerator and denominator, we get

$\rm \:  =  \:  \: \dfrac{ \red{5 \times {5}^{x}} \: (5 \: - \: 6)}{ \blue{{5}^{x}}(13 - 2 \times 5)}$

$\rm \:  =  \:  \: \dfrac{ 5\: ( - 1)}{(13 - 10)}$

$\rm \:  =  \:  \: - \: \dfrac{5}{3}$

Hence,

$\bf :\longmapsto\:\dfrac{ {5}^{x + 2} - 6 \times {5}^{x + 1} }{13 \times {5}^{x} - 2 \times {5}^{x + 1} } = - \: \dfrac{5}{3}$

Additional Information :-

$\boxed{ \sf \: {a}^{m - n} = {a}^{m} \div {a}^{n}}$

$\boxed{ \sf \: { ({a}^{n}) }^{m} = {a}^{nm}}$

$\boxed{ \sf \: {{a}^{0}} = 1}$

$\boxed{ \sf{ {a}^{0} = 1}}$