Prove that- xaxb c - xbxc a- xcxa b-1

LHS= ( x^ax^b )^c × ( x^bx^c )^a× ( x^cx^a )^b=1 LHS =x^ac× x^ab× x^bcx^bc× x^ac× x^ab (we can see that all the terms in the numerator and the denominator are ...

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Standard VIII

Mathematics

Powers with Unlike Bases and Same Exponent

Prove that, x...

Question

Prove that, ${(\frac{x^{a}}{x^{b}})}^{c} \times {(\frac{x^{b}}{x^{c}})}^{a} \times {(\frac{x^{c}}{x^{a}})}^{b} = 1$

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Solution

$L H S = {(\frac{x^{a}}{x^{b}})}^{c} \times {(\frac{x^{b}}{x^{c}})}^{a} \times {(\frac{x^{c}}{x^{a}})}^{b} = 1 L H S = \frac{x^{a c} \times x^{a b} \times x^{b c}}{x^{b c} \times x^{a c} \times x^{a b}}$
(we can see that all the terms in the numerator and the denominator are same)
LHS = 1 = RHS

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Similar questions

{(\frac{x^{a}}{x^{b}})}^{c} \times {(\frac{x^{b}}{x^{c}})}^{a} \times {(\frac{x^{c}}{x^{a}})}^{b}

=_______.

Q. Simplify

{(\frac{x^{a}}{x^{b}})}^{c} \times {(\frac{x^{b}}{x^{c}})}^{a} \times {(\frac{x^{c}}{x^{a}})}^{b}

Q. Simplify:

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

\times {(\frac{x^{c}}{x^{a}})}^{b}

\times {(\frac{x^{a}}{x^{b}})}^{c}

{(\frac{x^{a}}{x^{b}})}^{c} \times {(\frac{x^{b}}{x^{c}})}^{a} \times {(\frac{x^{c}}{x^{a}})}^{b}

is equal to

Prove that :

(i) ${(\frac{x^{a}}{x^{b}})}^{a^{2} + a b + b^{2}} \times {(\frac{x^{b}}{x^{c}})}^{b^{2} + a b + c^{2}} \times {(\frac{x^{c}}{x^{a}})}^{c^{2} + c a + a^{2}} = 1$

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

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Prove that, (xaxb)c×(xbxc)a×(xcxa)b=1

LHS=(xaxb)c×(xbxc)a×(xcxa)b=1LHS=xac×xab×xbcxbc×xac×xab (we can see that all the terms in the numerator and the denominator are same) LHS = 1 = RHS

Prove that, ${(\frac{x^{a}}{x^{b}})}^{c} \times {(\frac{x^{b}}{x^{c}})}^{a} \times {(\frac{x^{c}}{x^{a}})}^{b} = 1$

$L H S = {(\frac{x^{a}}{x^{b}})}^{c} \times {(\frac{x^{b}}{x^{c}})}^{a} \times {(\frac{x^{c}}{x^{a}})}^{b} = 1 L H S = \frac{x^{a c} \times x^{a b} \times x^{b c}}{x^{b c} \times x^{a c} \times x^{a b}}$
(we can see that all the terms in the numerator and the denominator are same)
LHS = 1 = RHS