Question

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Answer 1

$\mathsf{Given :\;\dfrac{-4}{\big[2187\big]^{\dfrac{-3}{7}}} - \dfrac{5}{\big[256\big]^{\dfrac{-1}{4}}} + \dfrac{2}{\big[1331\big]^{\dfrac{-1}{3}}}}$

☯  2187 can be written as 3⁷

☯  256 can be written as 4⁴

☯  1331 can be written as 11³

$\mathsf{\implies \dfrac{-4}{\big[3^7\big]^{\dfrac{-3}{7}}} - \dfrac{5}{\big[4^4\big]^{\dfrac{-1}{4}}} + \dfrac{2}{\big[11^3\big]^{\dfrac{-1}{3}}}}$

$\bigstar\;\;\textsf{We know that : \boxed{\mathsf{\big[a^m\big]^n = a^{mn}}}}$

$\mathsf{\implies \dfrac{-4}{\big[3\big]^{\bigg[7 \times \dfrac{-3}{7}\bigg]}} - \dfrac{5}{\big[4\big]^{\bigg[4 \times \dfrac{-1}{4}\bigg]}} + \dfrac{2}{\big[11\big]^{\bigg[3 \times \dfrac{-1}{3}\bigg]}}}$

$\mathsf{\implies \dfrac{-4}{\big[3\big]^{-3}} - \dfrac{5}{\big[4\big]^{-1}} + \dfrac{2}{\big[11\big]^{-1}}}$

$\bigstar\;\;\textsf{We know that : \boxed{\mathsf{\dfrac{1}{a^{-m}} = a^{m}}}}$

$\mathsf{\implies -4(3^3) - 5(4) + 2(11)}}$

$\mathsf{\implies -4(27) - 20 + 22}}$

$\mathsf{\implies -108 + 2}}$

$\mathsf{\implies -106}}$

Answer 2

Answer:

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