Question

show that:

show that X rays to a (b minus C )upon X raise to b (a minus c ) divided by (x raise to b upon X rays to a )whole to the power c equals to 1​

Answer 1

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Answer 2

TO PROVE :-

$\frac{ {x}^{a(b - c)} }{ {x}^{b(a - c)} } \div {(\frac{ {x}^{b} }{ {x}^{a} } ) }^{c} = 1$

PROOF :-

We shall solve it from LHS to get the RHS.

LHS =

$\frac{ {x}^{a(b - c)} }{ {x}^{b(a - c)} } \div {(\frac{ {x}^{b} }{ {x}^{a} } ) }^{c} \\ \\ \\ = \frac{ {x}^{ab - ac} }{ {x}^{ba - bc} } \div \frac{ {x}^{bc} }{ {x}^{ac} } \\ \\ \\ = {x}^{ab - ac - (ab - bc)} \div {x}^{bc - ac} \\ \\ \\ = {x}^{ab - ac - ab + bc} \div {x}^{bc - ac} \\ \\ \\ = {x}^{bc - ac} \div {x}^{bc - ac} \\ \\ \\ = \frac{ {x}^{bc - ac} }{ {x}^{bc - ac} } \\ \\ \\ = {x}^{bc - ac - (bc - ac)} \\ \\ \\ = {x}^{bc - ac - bc + ac} \\ \\ \\ = {x}^{0} \\ \\ \\ = 1$

= RHS

Hence Proved.

RULES :-

a^b * a^c = a^(b+c)

a^b ÷ a^c = a^(b - c)

a^0 = 1

(a^b)^c = a^(bc)