Question

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

Answer 1

Hi there!


`\frac {3^(-9) }{3^(-12) }` = 3⁻⁹ ⁺ ⁻¹² = 3⁻²¹=
`\frac {1}{3^(21) }`

EXPLANATION :-

•
`\frac {x^(m) }{x^(n) }` = xᵐ ⁺ ⁿ

Thus :-


`\frac {3^(-9) }{3^(-12) }` = 3⁻⁹ ⁺ ⁻¹²

• x⁻ᵐ =
`\frac {1}{x^(m) }`

Thus :-

3⁻²¹ =
`\frac {1}{3^(21) }`

Hence,
Option [B.] -
`\frac {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) }`