Question

Calculati
$\frac{(-3)^{-4}*27^{10} }{81^{9}*9^{-6} }$

Answer 1

$\frac{ {( - 3)}^{ - 4} \times {27}^{10} }{ {81}^{9} \times {9}^{ - 6} } = \frac{ \frac{1}{ {3}^{4} } \times {( {3}^{3} ) }^{10} }{{( {3}^{4} )}^{9} \times \frac{1}{ {( {3}^{2} )}^{6} } } = \frac{ \frac{1}{ {3}^{4} } \times {3}^{3 \times 10} }{ {3}^{4 \times 9} \times \frac{1}{ {3}^{2 \times 6} } }$

$= \frac{ \frac{1}{ {3}^{4} } \times {3}^{30} }{ {3}^{36} \times \frac{1}{ {3}^{12} } } = \frac{ \frac{ {3}^{30} }{ {3}^{4} } }{ \frac{ {3}^{36} }{ {3}^{12} } } = \frac{ {3}^{30 - 4} }{ {3}^{36 - 12} } = \frac{ {3}^{26} }{ {3}^{24} }$

$= {3}^{26 - 24} = {3}^{2} = 9$

Answer 2

( - 3) ⁻⁴ x 27 ¹⁰ = 1 / ( - 3) ⁴   x ( 3³ ) ¹⁰ = 1 / 3⁴   x  3 ³⁰ = 3 ³⁰ : 3⁴ = 3³⁰ ⁻ ⁴ = 3 ²⁶ ==> am calculat mai intai numaratorul

81⁹ x 9 ⁻⁶ = ( 3⁴ ) ⁹  x 1 / 9 ⁶  = 3³⁶  / 3¹²  = 3³⁶ ⁻ ¹²  = 3 ²⁴ == valoarea numitorului

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3 ²⁶  /  3²⁴ = 3 ²⁶ ⁻ ²⁴ = 3² = 9