what is the product of $(5m^{-2})(2m^{-3})$?\n$\frac{7}{m^{5}}$\n$7m^{6}$\n$\frac{10}{m^{5}}$\n$10m^{6}$

Explanation:

Step1: Multiply the coefficients

Multiply 5 and 2. $5\times2 = 10$

Step2: Multiply the variables with the same base

Use the rule $a^m\times a^n=a^{m + n}$. Here $a = m$, $m=- 2$ and $n=-3$. So $m^{-2}\times m^{-3}=m^{-2+( - 3)}=m^{-5}=\frac{1}{m^{5}}$

Step3: Combine the results

Multiply the result from step 1 and step 2. $10\times\frac{1}{m^{5}}=\frac{10}{m^{5}}$

Answer:

$\frac{10}{m^{5}}$