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.