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The value of \( \left( \frac { x ^ { a } } { x ^ { b } } \right) ^ { a ^ { 2 } + b ^ { 2 } + a b } \times \left( \frac { x ^ { b } } { x ^ { c } } \right) ^ { b ^ { 2 } + c ^ { 2 } + b c } \times \) \( \times \left( \frac { x ^ { b } } { x ^ { c } } \right) ^ { b ^ { 2 } + c ^ { 2 } + b c } \times \left( \frac { x ^ { c } } { x ^ { a } } \right) ^ { c ^ { 2 } + a ^ { 2 } + c a } \)

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Similar Questions

Q1

The value of

{(\frac{x^{a}}{x^{b}})}^{a^{2} + a b + b^{2}} \cdot {(\frac{x^{b}}{x^{c}})}^{b^{2} + b c + c^{2}} \cdot {(\frac{x^{c}}{x^{a}})}^{c^{2} + c a + b^{2}}

.

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Q2

Simplify :

{(\frac{x^{a}}{x^{b}})}^{a^{2} + a b + b^{2}} \times {(\frac{x^{b}}{x^{c}})}^{b^{2} + b c + c^{2}} \times {(\frac{x^{c}}{x^{a}})}^{c^{2} + c a + a^{2}}

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Q3

Prove that :
$$ \left ( \dfrac{x^{a}}{x^{b}} \right )^{a^{2}+ab+b^{2}}\times \left ( \dfrac{x^{b}}{x^{c}} \right )^{b^{2}+bc+c^{2}}\times \left ( \dfrac{x^{c}}{x^{a}} \right )^{c^{2}+ca+a^{2}} = 1 $$

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Q4

State true or false

Simplified form of

(\frac{x^{a}}{x^{b}})^{a^{2} + a b + b^{2}} \times (\frac{x^{b}}{x^{c}})^{b^{2} + b c + c^{2}} \times (\frac{x^{c}}{x^{a}})^{c^{2} + c a + a^{2}}

is 1

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Q5

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

equals

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