Question

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

Answer 1

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!

Answer 2

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
${g}^{ - a} = \frac{1}{ {g}^{a} } \: \: so \: \: \: {3}^{ - 21} = \frac{1}{ {3}^{21} }$