Question

How to solve this plss frac{(\sqrt{(3)})^{5}}{((\sqrt{(3)})^{-4})}=(\sqrt{(3)})^{(2k+1)​

Answer 1

Answer:

k = 4

Step-by-step explanation:

Given equation:

$\dfrac{(\sqrt{3})^{5}}{(\sqrt{3})^{-4}}=(\sqrt{3})^{(2k+1)}$

$\textsf{Apply exponent rule} \quad \dfrac{a^b}{a^c}=a^{b-c}:$

$\implies (\sqrt{3})^{(5-(-4))}=(\sqrt{3})^{(2k+1)}$

$\implies (\sqrt{3})^{9}=(\sqrt{3})^{(2k+1)}$

$\textsf{Apply exponent rule} \quad a^{f(x)}=a^{g(x)} \implies f(x)=g(x):$

$\implies (\sqrt{3})^{9}=(\sqrt{3})^{(2k+1)}$

$\implies 9=2k+1$

$\implies 2k=8$

$\implies k=4$