Which expression is equivalent to 12k^10m^-3/3k^2m^6

Answer 1

To simplify the expression \(\frac{12k^{10}m^{-3}}{3k^{2}m^{6}}\), we will divide the coefficients and then apply the properties of exponents.

1. Divide the coefficients: \[ \frac{12}{3} = 4 \]

2. Apply the laws of exponents to \(k\): \[ k^{10} \div k^{2} = k^{10-2} = k^{8} \]

3. Apply the laws of exponents to \(m\): \[ m^{-3} \div m^{6} = m^{-3-6} = m^{-9} \]

4. Combine the results: Putting it all together, we have: \[ 4k^{8}m^{-9} \]

Since \(m^{-9}\) can be written as \(\frac{1}{m^{9}}\), we can also express the final result as: \[ \frac{4k^{8}}{m^{9}} \]

Thus, the expression equivalent to \(\frac{12k^{10}m^{-3}}{3k^{2}m^{6}}\) is: \[ 4k^{8}m^{-9} \quad \text{or} \quad \frac{4k^{8}}{m^{9}} \]