Apply the Property of Negative Integer Exponents to generate an expression equivalent to 5^-9/4^-12 with positive exponents
only. (1 point)
Using the property of negative exponents, we can rewrite $5^{-9}$ as $\frac{1}{5^{9}}$ and $4^{-12}$ as $\frac{1}{4^{12}}$.
Therefore, the expression $5^{-9}/4^{-12}$ is equivalent to $\frac{\frac{1}{5^{9}}}{\frac{1}{4^{12}}}$.
To simplify this expression and get positive exponents, we can use the property of dividing fractions by multiplying by the reciprocal.
So, $\frac{\frac{1}{5^{9}}}{\frac{1}{4^{12}}}$ is equal to $\frac{1}{5^{9}} \cdot \frac{4^{12}}{1}$.
Multiplying powers with the same base involves adding the exponents, so we have $\frac{1}{5^{9}} \cdot 4^{12} = 4^{12}/5^{9}$.
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, you can rewrite the expression with positive exponents by reciprocating the fractions:
5^-9/4^-12
Using the property of negative exponents, we can rewrite it as:
(1/5^9)/(1/4^12)
To simplify this expression, we need to multiply by the reciprocal of the denominator, which is equivalent to dividing the numerator by the denominator:
(1/5^9) * (4^12/1)
Simplifying further:
(4^12)/(5^9)
So, the expression equivalent to 5^-9/4^-12 with positive exponents only is (4^12)/(5^9).