Thomas states: "A positive exponent is the number of times you multiply the base. A negative exponent is the number of times you divide by the base. "Do you agree? Explain your answer.
 

The development of the current metric system of units began in France in the 18th century. Basic units for measurements like angles, lengths, mass, and capacity were created, often derived from the properties of natural objects such as water. For example, $1$ liter of water has a mass of $1$kg. Multiples or divisions of these units could be created by using prefixes, such as those used in the units millimetre and kilogram. Some of the prefixes are given in the table below. Copy and complete the table.

If $5^6\times 5^3=5^k$, then find the value of $k$.

After simplifying $6^2\times 6^{-6}$ if we get $6^{\frac{1}{k}}$, then find the value of $k$.

After simplifying, $8^{-6}\times 8^2$ if we get $8^{\frac{1}{k}}$, then find the value of $k$.

If $\frac{x^9}{x^4}=x^k$, then find the value of $k$.

If $\frac{y^3}{y^{-2}}=y^k$, then find the value of $k$.

If $\frac{s^8}{s^{-3}}=s^k$, then find the value of $k$.

After simplifying, $\frac{{10}^{-3}}{{10}^4}$ if we get $\frac{1}{{10}^k}$, then find the value of $k$.