Question

Στο μο Ο Ο απ 3 6 12 27

Answer 1

Answer:

n = 12

Step-by-step explanation:

Given function:

$\dfrac{a^n}{a^3}=a^9$

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

$\implies a^{n-3}=a^9$

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

$\implies n-3=9$

Add 3 to both sides:

$\implies n-3+3=9+3$

$\implies n=12$

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Answer 2

Answer:

n = 12

Step-by-step explanation:

Given expression:

$\dfrac{a^n}{a^3} = a^9$

multiply both sides by a³

$\dfrac{a^n}{a^3} \times a^3 = a^9 \times a^3$

simplify following

$a^n = a^9 \times a^3$

apply indices law

$a^n = a^{9+3}$

simplify

$a^n = a^{12}$

compare powers

$n = 12$