Question

$<b>$
Solve this question
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Answer 1

Answer:

$\sqrt[bc]{\dfrac{x^{a^2}}{x^{bc}}}\times \sqrt[ac]{\dfrac{x^{b^2}}{x^{ac}}} \times \sqrt[bc]{\dfrac{x^{c^2}}{x^{ab}}}\\\implies \dfrac{x^{a^2/bc}}{x}\times \dfrac{x^{b^2/ac}}{x} \times \dfrac{x^{c^2/ab}}{x}\\\\\implies \dfrac{x^{a^2/bc+b^c/ac+c^2/ab}}{x^3}\\\\\implies \dfrac{x^{(a^3+b^3+c^3)/abc}}{x^3}\\\\\implies \dfrac{x^{3abc/abc}}{x^3}\\\\\implies \dfrac{x^3}{x^3}\\\\\implies 1$

Step-by-step explanation:

We know that when a + b + c = 0 , then a³ + b³ + c³ = 3 abc .

Also we know that :

$\sqrt[n]{x} = x^{\dfrac{1}{n}}$

Use the formula of :

$(\dfrac{x}{y})^n=\dfrac{x^n}{y^n}$

Using the law of indices , we can easily solve the question.

The sum law of indices add the powers when we are multiplying .

$a^b\times a^c=a^{b+c}$