Question

Find the value of 3/7∧−2 × 7/6∧−3

Answer 1

Step-by-step explanation:

Use Negative Power Rule: $\sf{x}^{-a}=\frac{1}{{x}^{a}}$

$\sf \red{ \implies\frac{1}{ \bigg(\frac{3}{7} \bigg){}^{2} } \times \frac{1}{ \bigg( \frac{7}{6} \bigg) {}^{3} } }$

$\sf \pink{ \implies \frac{1}{ \frac{9}{49} } \times \frac{1}{ \frac{343}{216} } }$

$\sf \purple{ \implies \frac{49}{9} \times \frac{1}{ \frac{343}{216} } }$

$\sf \blue{ \implies \frac{49}{ \frac{9 \times 343}{216} } }$

$\sf \orange{ \implies \frac{49}{ \frac{343}{24} } }$

$\sf \pink{ \implies49 \times \frac{24}{343} }$

$\bf \red{ \implies \frac{1176}{343} }$

$\red{\boxed {\underline {\bf \blue{ \pink\implies \frac{24}{7} }}}}$

$\boxed{ \tt \orange{Decimal \: \: Form: 3.428571}}$

Answer 2

Question :

.

$1) \: \frak{ \green{( \frac{3}{7}) {}^{ - 2} \times ( \frac{7}{6}) {}^{ - 3} }}$

$2) \: \frak{ \purple{( {3}^{2} + {2}^{2} ) \times ( \frac{1}{2}) {}^{ 3} }}$

Answer :

$1) \: \frak{ \pink{( \frac{7}{3}) {}^{ 2} \times ( \frac{6}{7}) {}^{ 3} }}$

$= \frak{ \pink{( \frac{49}{9}) \times ( \frac{216}{343}) }}$

$= \frak{ \pink{( \frac {\cancel{{49}} \: \green{1}}{ \cancel{{9}} \: \orange{1}}) \times ( \frac{ \cancel{{216}} \: \orange{24}}{ \cancel{{343}} \: \green{7}}) }}$

$\underline{\boxed{ \frak{ \purple{ \frac{24}{7} }}}} \star$

$2) \: \frak{ \red{( 9 + 4 ) \times ( \frac{1}{8}) }}$

$= \frak{ \red{13 \times \frac{1}{8} }}$

$\underline{\boxed{ \frak{ \purple{ \frac{13}{8} }}}} \star$