Question

Evaluate: x^a+b * x^b+c * x^c+a/(x^a * x^b * x^c)^2

Answer 1

ANSWER:

To Evaluate:

$\displaystyle \dfrac{x^{a+b}\times x^{b+c}\times x^{c+a}}{(x^a \times x^b \times x^c)^2}$

Solution:

We are given that,

$\displaystyle \implies\dfrac{x^{a+b}\times x^{b+c}\times x^{c+a}}{(x^a \times x^b \times x^c)^2}$

We know that,

$\hookrightarrow m^p\times m^q = m^{p+q}$

So,

$\displaystyle \implies\dfrac{x^{a+b}\times x^{b+c}\times x^{c+a}}{(x^a \times x^b \times x^c)^2}$

$\displaystyle \implies\dfrac{x^{a+b+b+c+c+a}}{(x^{a+b+c})^2}$

We know that,

$\hookrightarrow (m^p)^q= m^{pq}$

So,

$\displaystyle \implies\dfrac{x^{2(a+b+c)}}{(x^{a+b+c})^2}$

$\displaystyle \implies\dfrac{x^{2(a+b+c)}}{x^{2(a+b+c)}}$

Cancelling numerator and denominator,

$\displaystyle \implies\dfrac{x^{2(a+b+c)}}{x^{2(a+b+c)}}$

$\displaystyle \implies\bf 1$

Hence,

$\displaystyle \implies\bf\dfrac{x^{a+b}\times x^{b+c}\times x^{c+a}}{(x^a \times x^b \times x^c)^2}=1$

Formula Used:

• $\hookrightarrow m^p\times m^q = m^{p+q}$
• $\hookrightarrow (m^p)^q= m^{pq}$