Question

find the value of x^a-b*x^b-c*x^c-a class 9

Answer 1

$\displaystyle \sf{ {x}^{a - b} \times {x}^{b - c} \times {x}^{c - a} } = 1$

Given :

$\displaystyle \sf{ {x}^{a - b} \times {x}^{b - c} \times {x}^{c - a} }$

To find :

The value of the expression

Formula :

$\sf{1. \: \: {a}^{m} \times {a}^{n} = {a}^{m + n} }$

$\displaystyle \sf{2. \: \: {a}^{0} = 1}$

Solution :

Step 1 of 2 :

Write down the given expression

Here the given expression is

$\displaystyle \sf{ {x}^{a - b} \times {x}^{b - c} \times {x}^{c - a} }$

Step 2 of 2 :

Find the value of the expression

$\displaystyle \sf{ {x}^{a - b} \times {x}^{b - c} \times {x}^{c - a} }$

$\displaystyle \sf{ = {x}^{(a - b) + (b - c) + (c - a)} }\: \: \: \bigg[ \: \because \: {a}^{m} \times {a}^{n} = {a}^{m + n}\bigg]$

$\displaystyle \sf{ = {x}^{(a - b+ b - c + c - a)} }$

$\displaystyle \sf{ = {x}^{0} }$

$\displaystyle \sf{ = 1\: \: \: \bigg[ \: \because \:{a}^{0} = 1 \bigg] }$

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