Question

[(2/13)^-6÷(2/13)^3]^3×(2/13)^-9

Answer 1

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Here is u r Ans ➡

✨
$= (( \frac{2}{13} {}^{ - 6} \div ( \frac{2}{1 3} ) {}^{3} ) {}^{3} \times ( \frac{2}{13} ) {}^{ - 9}$

$= using \: > \: ( \frac{a}{b} ) {}^{ - n} = ( \frac{b}{a} ) {}^{n}$

$= (( \frac{23}{2} ) {}^{6} ) \div \frac{8}{2197} ) {}^{3} \times ( \frac{13}{2}) {}^{9}$

$= ( \frac{23 {}^{6} }{2 {}^{6} } \times \frac{2197}{8} ) {}^{3} \times \frac{13 {}^{9} }{2 {}^{9} }$

$= \frac{23 {}^{18} }{2 {}^{18} } \times ( \frac{2197}{8} ) {}^{3} \times \frac{13 {}^{9} }{2 {}^{9} }$

$= \frac{23 {}^{18} }{2 {}^{18} } \times \frac{2197 {}^{3} }{8 {}^{3} } \times \frac{13 {}^{9} }{2 {}^{9} }$

$= \frac{23 {}^{18} \times 2197 {}^{3} \times 13 {}^{9} }{2 {}^{27} \times 8 {}^{3} }$
$= \frac{23 {}^{18} \times 13 {}^{9} \times 13 {}^{9} }{2 {}^{27} \times 2 {}^{9} }$

$= \frac{299 {}^{18} }{2 {}^{36} }$

$= in \: decimal \: form \: > \: 5.30886 \times 10 {}^{33}$
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