Talei says: "Negative exponents make fractions. If the negative exponent is already in the denominator of a fraction, then it makes an integer." Is Talei correct? Explain.

 

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 $k$.