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Expansion of (x-y)^2

x ∧ a / x ∧ b...

Question

(x^a/x^b)^1/ab . (x^b/x^c)^1/bc . (x^c/x^a)^1/ca

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Solution

Consider LHS:

= $x to the power of fraction numerator a over denominator a b end fraction minus fraction numerator b over denominator a b end fraction end exponent space x to the power of fraction numerator b over denominator b c end fraction minus fraction numerator c over denominator b c end fraction end exponent space x to the power of fraction numerator c over denominator a c end fraction minus fraction numerator a over denominator a c end fraction end exponent$

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Similar questions

Q. Solve the following equations :
(a)

\frac{x - a}{b c} + \frac{x - b}{c a} + \frac{x - c}{a b}

(\frac{1}{a} + \frac{1}{b} + \frac{1}{c})

\frac{(x - a) (x - b)}{x - a - b} = \frac{(x - c) (x - d)}{x - c - d}

How to prove (x^a÷x^b)^1÷ab (x^b÷x^c)^1÷bc (x^c÷x^a)^1÷ca

Q. Prove that

(i)

\sqrt{x^{- 1} y} \cdot \sqrt{y^{- 1} z} \cdot \sqrt{z^{- 1} x} = 1

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

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

\frac{{(x^{a + b})}^{2} {(x^{b + c})}^{2} {(x^{c + a})}^{2}}{{(x^{a} x^{b} x^{c})}^{4}} = 1

Q. State whether the statement is True or False.

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

Q. Prove that :

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

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