Question

Apply the Property of Negative Integer Exponents to generate an expression equivalent to 5^-9/4^-12 with only positive exponents.

Answer 1

To convert the expression 5^-9/4^-12 into an expression with only positive exponents, we can apply the property of negative integer exponents, which states that a^(-b) is equal to 1/a^b.

Using this property, we can rewrite 5^-9 as 1/5^9 and 4^-12 as 1/4^12. Therefore, the expression becomes:

(1/5^9)/(1/4^12)

Next, we can simplify this expression further by multiplying the numerator and denominator by the reciprocal of the denominator, which is 4^12. This reciprocal is equivalent to 1/4^12, so we have:

(1/5^9) * (4^12/1)

Now, we multiply the numerators and denominators separately:

(1 * 4^12) / (5^9 * 1)

This simplifies to:

4^12 / 5^9

Hence, the expression equivalent to 5^-9/4^-12 with only positive exponents is 4^12 / 5^9.