For any positive real number x- write the value of xab1-abxbc1-bcxca1-ca

{ (x^a)^b}^1/ab{(x^b)^c}^1/bc{(x^c)^a}^1/ca =(x^ab )^1/ab.(x^bc )^1/bc.(x^ca )^1/ca =x^ab/ab.x^bc/bc.x^ca/ca =x^1× x^1× x^1 = x × x × x = x^3 ...

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Byju's Answer

Standard IX

Mathematics

Laws of Exponents for Real Numbers

For any posit...

Question

For any positive real number x, write the value of

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

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Solution

${(x^{a})^{b}}^{\frac{1}{a b}} {(x^{b})^{c}}^{\frac{1}{b c}} {(x^{c})^{a}}^{\frac{1}{c a}} = {(x^{a b})}^{\frac{1}{a b}} . {(x^{b c})}^{\frac{1}{b c}} . {(x^{c a})}^{\frac{1}{c a}} = x^{\frac{a b}{a b}} . x^{\frac{b c}{b c}} . x^{\frac{c a}{c a}} = x^{1} \times x^{1} \times x^{1} = x \times x \times x = x^{3}$

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For any positive real number x, write the value of {(xa)b}1ab{(xb)c}1bc{(xc)a}1ca

{(xa)b}1ab{(xb)c}1bc{(xc)a}1ca=(xab)1ab.(xbc)1bc.(xca)1ca=xabab.xbcbc.xcaca=x1×x1×x1=x×x×x=x3

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