Question

Apply the property of negative integer exponents to generate an expression equivalent to 5^-9/4^-12 with positve exponents only.

Answer 1

To apply the property of negative integer exponents, we can move the negative exponents to the numerator and change their signs to positive exponents.

Starting with the expression 5^(-9) / 4^(-12), we can rewrite it as (1 / 5^9) / (1 / 4^12).

Now, let's simplify this expression further.

Using the property of dividing fractions, we can rewrite (1 / 5^9) / (1 / 4^12) as (1 / 5^9) * (4^12 / 1).

Applying the property of positive exponents, we can rewrite 5^9 as (1 / 5^-9) and 4^12 as (1 / 4^-12).

Therefore, (1 / 5^9) * (4^12 / 1) becomes (1 / 5^-9) * (1 / 4^-12).

Combining the two fractions, we get 1 / (5^-9 * 4^-12).

Now, let's apply the property of multiplying exponents with the same base.

We have 5^-9 * 4^-12 = (5 * 4)^-9/-12 = 20^-9/12.

Finally, we rewrite 20^-9/12 as (1 / 20^9)^(1/12).

So, the expression equivalent to 5^-9/4^-12 with positive exponents only is (1 / 20^9)^(1/12).