Apply the Property of Negative Integer Exponents to generate an expression equivalent to 5^−9/4^−12

Question

with positive exponents only.

Answer 1

To eliminate the negative integer exponents in the expression \( \frac{5^{-9}}{4^{-12}} \), we can apply the property of negative exponents, which states that \( a^{-n} = \frac{1}{a^n} \).

Starting with the given expression:

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

We can rewrite this using the property of negative exponents:

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

Using the division of fractions, we can multiply by the reciprocal:

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

This can be written as:

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

Finally, we have an expression with positive exponents only:

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

This expression \( \frac{4^{12}}{5^{9}} \) is the equivalent expression with only positive exponents.

Answer 2

5^-9/4^-12=

Answer 3

To simplify the expression \( \frac{5^{-9}}{4^{-12}} \), we can apply the property of negative exponents, which states that \( a^{-n} = \frac{1}{a^n} \).

Starting with the expression:

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

We can rewrite the negative exponents:

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

When dividing by a fraction, we can multiply by its reciprocal:

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

This can also be expressed as:

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

So, the simplified form of the expression \( \frac{5^{-9}}{4^{-12}} \) is:

\[ \frac{4^{12}}{5^9} \]