### Video Transcript

Simplify ๐ฅ to the power six divided by ๐ฅ to the power four.

In order to answer this question, we need to know the laws of exponents or indices. If we wish to divide two terms with the same base, in this case the letter ๐ฅ, then we need to subtract their exponents or powers. This is due to the fact that one of the laws of exponents states that ๐ฅ to the power ๐ divided by ๐ฅ to the ๐ is equal to ๐ฅ to the power of ๐ minus ๐.

In our example, six minus four equals two. Therefore, ๐ฅ to the power six divided by ๐ฅ to the power four equals ๐ฅ to the power of two. This is a pretty straightforward example. But the law can be extended to deal with fractional exponents or negative exponents.

For example, ๐ฅ to the power four divided by ๐ฅ to the power of negative two can be rewritten as ๐ฅ to the power of four minus negative two. As four minus negative two is six, our answer is ๐ฅ to the power of six.

In the same way, if the exponents or powers are fractions, we can subtract the two fractions. ๐ฅ to the power of seven over 11 divided by ๐ฅ to the power of three over 11 equals ๐ฅ to the seven over 11 minus three over 11, which gives us an answer of ๐ฅ to the four over 11 or four 11ths.