Question

simplify x power p whole divided by x power q whole to the power of p+q multiplied to x power q whole divided by x power of q+p multiplied to x power r whole divided by x power p whole to the power of r+p

Answer 1

To find:

We have to simplify the following term,

$\mathsf{(\dfrac{x^{p}}{x^{q}})^{p+q}\times (\dfrac{x^{q}}{x^{r}})^{q+r}\times (\dfrac{x^{r}}{x^{p}})^{r+p}}$

Method:

Before we solve the problem, let us know some rules,

• $\mathsf{\dfrac{a^{b}}{a^{c}}=a^{b-c}}$

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

• $\mathsf{(a^{b})^{c}=a^{bc}}$

• $\mathsf{a^{0}=1}$

• $\mathsf{(a+b)(a-b)=a^{2}-b^{2}}$

Step-by-step explanation:

Now, $\mathsf{(\dfrac{x^{p}}{x^{q}})^{p+q}\times (\dfrac{x^{q}}{x^{r}})^{q+r}\times (\dfrac{x^{r}}{x^{p}})^{r+p}}$

$\mathsf{=(x^{p-q})^{p+q}\times (x^{q-r})^{q+r}\times (x^{r-p})^{r+p}}$

$\mathsf{=x^{(p-q)(p+q)}\times x^{(q-r)(q+r)}\times x^{(r-p)(r+p)}}$

$\mathsf{=x^{p^{2}-q^{2}}\times x^{q^{2}-r^{2}}\times x^{r^{2}-p^{2}}}$

$\mathsf{=x^{p^{2}-q^{2}+q^{2}-r^{2}+r^{2}-p^{2}}}$

$\mathsf{=x^{0}}$

$\mathsf{=1}$

Answer:

$\mathsf{(\dfrac{x^{p}}{x^{q}})^{p+q}\times (\dfrac{x^{q}}{x^{r}})^{q+r}\times (\dfrac{x^{r}}{x^{p}})^{r+p}=1}$

Answer 2

This is your answer..

Hope it will help you..