Respuesta :

MarkV
Hi there!

[tex] \frac{ {3}^{ - 9} }{ {3}^{ - 12} } = {3}^{ - 9 + - 12} = {3}^{ - 21} = \frac{1}{ {3}^{21} } [/tex]

The answer is B.

Explanation.

1st step.
[tex] \frac{ {g}^{a} }{ {g}^{b} } = {g}^{a - b} \: \: so \: \: \: \frac{ {3}^{ - 9} }{ {3}^{ - 12} } = {3}^{ - 9 + - 12} \: [/tex]

2nd step
[tex] {g}^{ - a} = \frac{1}{ {g}^{a} } \: \: so \: \: \: {3}^{ - 21} = \frac{1}{ {3}^{21} } [/tex]
VictorZ
Hi there!

[tex]\dfrac {3^{-9} }{3^{-12} }[/tex] = 3⁻⁹ ⁺ ⁻¹² = 3⁻²¹= [tex]\dfrac {1}{3^{21} }[/tex]

EXPLANATION :-

• [tex]\dfrac {x^{m} }{x^{n} }[/tex] = xᵐ ⁺ ⁿ

Thus :-

[tex]\dfrac {3^{-9} }{3^{-12} }[/tex] = 3⁻⁹ ⁺ ⁻¹²

• x⁻ᵐ = [tex]\dfrac {1}{x^{m} }[/tex]

Thus :-

3⁻²¹ = [tex]\dfrac {1}{3^{21} }[/tex]

Hence,
Option [B.] - [tex]\dfrac {1}{3^{21} }[/tex] is Correct

~ Hope it helps!
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