Question

(4/2184^-3/7)-(5/256^-1/4)+(2/(1331^2)^-1/3)



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Answer 1

(4/2184^-3/7)-(5/256^-1/4)+(2/(1331^2)^-1/3)

=(2184/4)^3/7-(256/5)¼+(1771561/2)⅓

=546^3/7-(51.2)¼+(885780.5)⅓

Answer 2

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

•  2187 can be written as 3⁷
•   256 can be written as 4⁴
• 1331 can be written as 11³

Solution :-

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

• $\;\;\textsf{ \red{\boxed{\mathsf{\big[a^m\big]^n = a^{mn}}}}}$

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

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

• $\;\;\textsf{ \red{\boxed{\mathsf{\dfrac{1}{a^{-m}} = a^{m}}}}}$

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

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

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

$\mathsf{\: \: \: \: \: \: \:\pink{ \::\implies -106}}$

$\therefore\:\underline{\textsf{ Required value is \textbf{-106}}}.$