Question

by what number should (-6) power -1 be multiplied so that the product is 9 power -1​

Answer 1

$\underbrace{ \underline{ \boxed{ \tt \red\star \pink{SOLUTION}}}}$

$\tt Let \: the \: no. \: which \: is \: to \: be \: multiplied \: be \: x$

$\tt Now,$

$\mathcal{ACCORDING \: TO \: QUESTION}$

$\tt so,$

$\tt \longrightarrow {( - 6)}^{ - 1} \times x = {(9)}^{ - 1}$

$\tt \bigstar we \: know \: ({ \frac{a}{b} )}^{ - 2} = ({ \frac{b}{a}) }^{2}$

$\tt so,$

$\tt \longrightarrow \frac{ - 1}{6} \times x = \frac{1}{9}$

$\tt \longrightarrow x = \frac{1}{9} \times ( - 6)$

$\tt \longrightarrow x = \frac{ \cancel{- 6}}{ \cancel9} = \frac{ - 2}{3}$

$\star \longrightarrow \boxed{ \tt x = \frac{ - 2}{3} }$

Answer 2

Answer:

$\huge\underline\bold \red {♡AnswEr♡}</p><p>$

$\tt Let \: the \: no. \: which \: is \: to \: be \: multiplied \: be \: x$

$\tt \longrightarrow {( - 6)}^{ - 1} \times x = {(9)}^{ - 1}⟶(−6) </p><p>−1</p><p> ×x=(9) </p><p>−1$

$\: ({ \frac{a}{b} )}^{ - 2} = ({ \frac{b}{a}) }^{2}$

$\tt so</p><p></p><p>\tt \longrightarrow \frac{ - 1}{6} \times x = \frac{1}{9}⟶ </p><p>6</p><p>−1$

$\tt \longrightarrow x = \frac{1}{9} \times ( - 6)⟶x= </p><p>9</p><p>1$

×(−6)

$\tt \longrightarrow x = \frac{ \cancel{- 6}}{ \cancel9} = \frac{ - 2}{3}⟶x= </p><p>9</p><p> </p><p> </p><p>−6</p><p> </p><p> </p><p> </p><p> = </p><p>3</p><p>−2$

${ \tt x = \frac{ - 2}{3} }⋆⟶$