Question

P+p²+p³+p⁴+p⁵+p⁶+p⁷)/(p⁻³+p⁻⁴+p⁻⁵+p⁻⁶+p⁻⁷+p⁻⁸+p⁻⁹)​

Answer 1

Answer:

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Answer 2

$\underline \pink{\textsf{Given:}}$

$\bold\red{\mathsf{\dfrac{p+p^2+p^3+p^4+p^5+p^6+p^7}{p^{-3}+p^{-4}+p^{-5}+p^{-6}+p^{-7}+p^{-8}+p^{-9}}}}$

$\underline \green{\textsf{To find:}}\textsf \blue{The value of}$

$\mathsf \purple{\dfrac{p+p^2+p^3+p^4+p^5+p^6+p^7}{p^{-3}+p^{-4}+p^{-5}+p^{-6}+p^{-7}+p^{-8}+p^{-9}}} </p><p>$

$\underline \orange{\textsf{Solution:}}$

$\textsf \red{Consider,}$

$\mathsf \pink{\dfrac{p+p^2+p^3+p^4+p^5+p^6+p^7}{p^{-3}+p^{-4}+p^{-5}+p^{-6}+p^{-7}+p^{-8}+p^{-9}}}$

$\textsf \green{Multiply both numerator and denominator by}\,\mathsf{p^{10}}$

$\mathsf \orange{=\dfrac{p+p^2+p^3+p^4+p^5+p^6+p^7}{p^{-3}+p^{-4}+p^{-5}+p^{-6}+p^{-7}+p^{-8}+p^{-9}}{\times}\dfrac{p^{10}}{p^{10}}}$

$\mathsf \blue{=\dfrac{(p+p^2+p^3+p^4+p^5+p^6+p^7)p^{10}}{p^7+p^6+p^5+p^4+p^3+p^2+p}}$

$\mathsf\red{=\dfrac{(p+p^2+p^3+p^4+p^5+p^6+p^7)p^{10}}{p+p^2+p^3+p^4+p^5+p^6+p^7}}$

$\mathsf \blue{=p^{10}}$

$\underline \green{\textsf{Answer:}}$

$\mathsf \pink{\dfrac{p+p^2+p^3+p^4+p^5+p^6+p^7}{p^{-3}+p^{-4}+p^{-5}+p^{-6}+p^{-7}+p^{-8}+p^{-9}}=p^{10}}$