Question

simplify. express your answer using positive exponents.\\(\frac{m^{-7}}{m^{9}}\\)

Explanation:

Step1: Apply exponent rule for division

When dividing exponents with the same base, we subtract the exponents: $a^m \div a^n = a^{m - n}$. So for $\frac{m^{-7}}{m^{9}}$, we have $m^{-7 - 9}$.

Step2: Simplify the exponent

Calculate $-7 - 9 = -16$, so we get $m^{-16}$.

Step3: Convert to positive exponent

Using the rule $a^{-n} = \frac{1}{a^n}$, we convert $m^{-16}$ to $\frac{1}{m^{16}}$.

Answer:

$\frac{1}{m^{16}}$