Question

plese answer this math question​

Answer 1

Answer:true

hope now it's clear to u ...

Answer 2

$\purple{\large{\underline{\underline{ \rm{Question: }}}}}$

$\sf{ { z}^{a - b} \times {z}^{a - c} \times {z}^{c - a} = 1 }$

$\purple{\large{\underline{\underline{ \rm{Answer: }}}}}$

$\sf{ \blue{True ✔}}$

$\purple{\large{\underline{\underline{ \rm{Explanation:- }}}}}$

$\sf{z}^{a - b} \times {z}^{b - a} \times {z}^{c - a}$

When bases are same with multiplication sign between then, we add the powers or exponents, taking base common for all the powers.

$\sf {z}^{a - b +b - c +c - a}$

Opposite signs cancel each other, we have:

$\sf {z}^{0}$

Any non-zero number raised to the power zero is always equal to unity i.e., 1.

$\sf{ \therefore{ \sf{ \blue{ \underline{ \boxed{ {z}^{ 0} = 1}}}}}}$

L.H.S = R.H.S

$\sf{ \blue{ </strong><strong>Hence</strong><strong> \: </strong><strong>Proved</strong><strong>!</strong><strong>!</strong><strong>}}$

━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━