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

only. (1 point)

1 answer

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 $4^{12}/5^{9}$.