Apply the Property of Negative Integer Exponents to generate an expression equivalent to 5^−9/4^−12 with positive exponents only.
To apply the Property of Negative Integer Exponents, we can rewrite 5^(-9) as 1/5^9 and 4^(-12) as 1/4^12.
So, the expression 5^(-9)/4^(-12) can be written as (1/5^9)/(1/4^12).
Now, to simplify this expression and get positive exponents only, we can use the property of dividing fractions by multiplying by the reciprocal.
Therefore, (1/5^9)/(1/4^12) = (1/5^9) * (4^12/1).
Simplifying further, we can write this as 4^12/5^9 with positive exponents only.
To apply the property of negative integer exponents, we can rewrite the expression 5^−9/4^−12 with positive exponents.
The property states that any base raised to a negative exponent can be rewritten by taking the reciprocal of the base raised to the positive exponent.
So, we can rewrite 5^−9 as 1/5^9 and 4^−12 as 1/4^12.
Using this property, the expression 5^−9/4^−12 becomes:
(1/5^9)/(1/4^12)
Now, to divide by a fraction, we invert the second fraction and multiply:
(1/5^9) * (4^12/1)
Simplifying further, we have:
4^12 / 5^9
Therefore, the expression equivalent to 5^−9/4^−12 with positive exponents only is 4^12 / 5^9.
To apply the property of negative integer exponents, we can rewrite the expression with positive exponents by moving the base with the negative exponent to the denominator and changing the sign of the exponent.
Let's start with the expression 5^(-9) / 4^(-12).
Step 1: Move 5^(-9) to the denominator.
So, the expression becomes 1 / 5^(9) * 4^(-12).
Step 2: Change the sign of the exponents.
The expression now becomes 1 / 5^(9) * 1 / 4^(12).
Step 3: Simplify the exponents.
Since 5^(-9) is in the denominator, it becomes 1 / 5^(9), and since 4^(-12) is already in the denominator, it remains the same.
Therefore, the expression equivalent to 5^(-9) / 4^(-12) with positive exponents only is 1 / (5^(9) * 4^(12)).