Question

Apply the Property of Negative Integer Exponents to generate an exponents to 5-⁹/4-¹² with positive exponents only. (1 point)

5-⁹/4-¹²= blank

Answer 1

To apply the property of negative integer exponents, we can use the rule that states:

\[
a^{-n} = \frac{1}{a^{n}}
\]

This means that we can convert negative exponents to positive exponents by taking the reciprocal.

Let's apply this to \(5^{-9}/4^{-12}\):

1. Convert \(5^{-9}\) to positive exponent:
\[
5^{-9} = \frac{1}{5^9}
\]

2. Convert \(4^{-12}\) to positive exponent:
\[
4^{-12} = \frac{1}{4^{12}}
\]

Now, rewrite the expression \(5^{-9}/4^{-12}\):

\[
\frac{5^{-9}}{4^{-12}} = \frac{\frac{1}{5^9}}{\frac{1}{4^{12}}}
\]

Dividing by a fraction is equivalent to multiplying by its reciprocal:

\[
= \frac{1}{5^9} \times 4^{12} = \frac{4^{12}}{5^9}
\]

Thus, we can write the expression with positive exponents only:

\[
5^{-9}/4^{-12} = \frac{4^{12}}{5^9}
\]

So fill in the blank:

\[
5^{-9}/4^{-12} = \frac{4^{12}}{5^9}
\]