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ArbitrLikvidat [17]
2 years ago
11

Simplify 3^-9/ 3^-12 a.1/3^3 b.1/3^21 c.3^3 d.3*21

Mathematics
2 answers:
dmitriy555 [2]2 years ago
8 0
Hi there!

\dfrac {3^{-9} }{3^{-12} } = 3⁻⁹ ⁺ ⁻¹² = 3⁻²¹= \dfrac {1}{3^{21} }

EXPLANATION :-

• \dfrac {x^{m} }{x^{n} } = xᵐ ⁺ ⁿ

Thus :-

\dfrac {3^{-9} }{3^{-12} } = 3⁻⁹ ⁺ ⁻¹²

• x⁻ᵐ = \dfrac {1}{x^{m} }

Thus :-

3⁻²¹ = \dfrac {1}{3^{21} }

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

~ Hope it helps!
VLD [36.1K]2 years ago
3 0
Hi there!

\frac{ {3}^{ - 9} }{ {3}^{ - 12} } = {3}^{ - 9 + - 12} = {3}^{ - 21} = \frac{1}{ {3}^{21} }

The answer is B.

Explanation.

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

2nd step
{g}^{ - a} = \frac{1}{ {g}^{a} } \: \: so \: \: \: {3}^{ - 21} = \frac{1}{ {3}^{21} }
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