Question

Considere como verdadeiras as igualdades $<var>A^{m-p} = 2 </var>$ e $<var>A^{3p} = 8</var>$.

Qual o valor de $<var>A^{m}</var>$?

 

a) 4

b) 6

c) 8

d) 10

Answer 1

é b pq a com 2 são 4 -1 são 3 com mais tres 6

Answer 2

$A^{m-p} = 2\\\\ A^{3(m-p)} = 2^{3}\\\\ A^{3p} = 8 \to 8 = 2^{3}\\\\ A^{3p} = 2^{3}\\\\ 2^{3} = 2^{3}\\\\ A^{3(m-p)} = A^{3p}\\\\ 3(m - p) = 3p\\\\ m - p = p\\\\ \boxed{m = 2p}\\\\ A^{m-p} = 2 \\\\ A^{2p-p} = 2 \\\\ A^{p} = 2\\\\ A^{m} = 2A^{p}\\\\ A^{m} = 2*2 = 4\\\\ \boxed{\boxed{A^{m} = 4}}$