Simplify 𝑥 to the power six divided by 𝑥 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 𝑥, then we need to subtract their exponents or powers. This is due to the fact that one of the laws of exponents states that 𝑥 to the power 𝑎 divided by 𝑥 to the 𝑏 is equal to 𝑥 to the power of 𝑎 minus 𝑏.
In our example, six minus four equals two. Therefore, 𝑥 to the power six divided by 𝑥 to the power four equals 𝑥 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, 𝑥 to the power four divided by 𝑥 to the power of negative two can be rewritten as 𝑥 to the power of four minus negative two. As four minus negative two is six, our answer is 𝑥 to the power of six.
In the same way, if the exponents or powers are fractions, we can subtract the two fractions. 𝑥 to the power of seven over 11 divided by 𝑥 to the power of three over 11 equals 𝑥 to the seven over 11 minus three over 11, which gives us an answer of 𝑥 to the four over 11 or four 11ths.