Question

Simplify 3 to the negative 9th power divided by 3 to the negative 12th power

Answer 1

3³ = 27

Step-by-step explanation:

using the rule of exponents

•
`(a^(m) )/(a^(n) )` =
`a^((m-n))`

given

`(3^(-9) )/(3^(-12) )`

=
`3^((-9-(-12)))`

=
`3^((-9+12))`

= 3³

= 27

Answer 2

To simplify 3 to the negative 9th power divided by 3 to the negative 12th power, subtract the exponents: -9 - (-12) = 3, resulting in 3 to the 3rd power, or 27.

Step-by-step explanation:

The student has asked how to simplify 3 to the negative 9th power divided by 3 to the negative 12th power.

To solve this, we can use the rules of exponents which state that to divide powers with the same base, you subtract the exponents.

In this case, we have 3-9 / 3-12. Applying the rule, we subtract the exponents: (-9) - (-12) = -9 + 12 = 3.

Thus, our expression simplifies to 3 to the 3rd power or 33, which equals 27.