Write an equivalent expression using negative exponents.

1/3^9
will i write this as 3^-9. please explain this to me.

yes

one of the rules of powers is that
(a/b)^-n = (b/a)^+n

we are simply following this rule

To write the expression 1/3^9 using negative exponents, we can start by understanding the relationship between negative exponents and reciprocals.

When a number is raised to a negative exponent, it is equivalent to taking the reciprocal of that number raised to the positive exponent.

Let's apply this concept to the given expression:

1/3^9

We can rewrite this expression as:

1/(3^9)

To convert the positive exponent to a negative exponent, we take the reciprocal of the base raised to the positive exponent.

The base here is 3, so the reciprocal of 3^9 is 1/(3^9).

Now, we can simplify this expression using a negative exponent:

1/(3^9) = 3^-9

So, the equivalent expression using negative exponents for 1/3^9 is 3^-9.