Question

simplify [p^(a-b)]^c x [p^(a-c)]^b x [p^(-a)]^a x [p^b]^c

Answer 1

$\underline{\textsf{To simplify:}}$

$\mathsf{[p^(a-b)]^c{\times}[p^(a-c)]^b{\times}[p^(-a)]^a{\times}[p^b]^c}$

$\underline{\textsf{Solution:}}$

$\textsf{Consider,}$

$\mathsf{[p^(a-b)]^c{\times}[p^(a-c)]^b{\times}[p^(-a)]^a{\times}[p^b]^c}$

$\textsf{Using}$

$\boxed{\mathsf{(a^m)^n=a^{mn}}}$

$\mathsf{=[p^{(a-b)c}]{\times}[p^{(a-c)b}]{\times}[p^(-a^2)]{\times}[p^{bc}]}$

$\mathsf{=[p^{ac-bc}]{\times}[p^{ab-bc}]{\times}[p^(-a^2)]{\times}[p^{bc}]}$

$\mathsf{=p^{ac-bc+ab-bc-a^2+bc}}$

$\mathsf{=p^{ac-bc+ab-a^2}}$

$\mathsf{=p^{c(a-b)-a(a-b)}}$

$\mathsf{=p^{(c-a)(a-b)}}$

$\underline{\textsf{Answer:}}$

$\mathsf{p^{(c-a)(a-b)}}$

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Answer 2

Answer:

p^(c-a)(a-b)

Step-by-step explanation:

its too long to explain bt i helped u by revealing the answer