Question

for what value of a does (1/7)^(3a+3)=343^(a-1)
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Answer 1

Answer:

a = 0

Step-by-step explanation:

$\left(\dfrac{1}{7}\right)^{3a+3}=343^{a-1}\qquad\text{use}\ a^{-n}=\left(\dfrac{1}{a}\right)^n\\\\7^{-(3a+3)}=(7^3)^{a-1}\qquad\text{use the distributive property}\\\\7^{-3a-3}=7^{3a-3}\iff-3a-3=3a-3\qquad\text{add 3 to both sides}\\\\-3a=3a\qquad\text{subtract}\ 3a\ \text{from both sides}\\\\-6a=0\qquad\text{divide both sides by (-6)}\\\\a=0$