Question 1

Can someone help me please

Question 2

Answer:

$\sf \frac{{x}^(a \: (b - c)) }{ {x}^(b \: (a - c)) } \: / \: \bigg \lgroup \frac{ {x}^(b) }{ {x}^(a) } \bigg \rgroup^(c) \: = \: 1$

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Now,

$\sf \frac{{x}^(ab \: - \: ac) }{ {x}^(ba \: - \: b c) } \: / \: \bigg \lgroup \frac{ ({x}^(b) )}{( {x}^(a)) } \bigg \rgroup^(c) \: = \: 1$

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$\sf \frac{{x}^(ab \: - \: ac) }{ {x}^(ba \: - \: b c) } \: / \: \frac{ {x}^(bc) }{{x}^(ac) } \: = \: 1$

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We know that, When sign change from division to multiplication we should do reciprocal of next number.

Therefore we get,

$\sf \frac{{x}^(ab \: - \: ac) }{ {x}^(ba \: - \: b c) } \: * \: \frac{ {x}^(ac) }{{x}^(bc) } \: = \: 1$

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$\sf \frac{{x}^{ab \: - \: \cancel {ac }\: + \: \cancel{ac}} }{ {x}^{ba \: - \: \cancel{ b c} \: + \: \cancel{bc}} } \: = \: 1$

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$\sf \frac{{x} \: ^{ \cancel{ab}} }{ {x} \: ^{\cancel{ba}} } \: = \: 1$

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$\bigstar \: \: \underline{ \boxed{\sf x \: = \: 1}} \: \: \bigstar$

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$\huge\bf \dag \: \gray{RHS = LHS} \: \dag$

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$\large \star \: \tt Hence, Verified \: \star$

Question 3

Explanation:

kindly see attached picture

hope it helped you:)

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