Video Transcript
True or false: The simplified form of 𝑥 to the power of negative four over 𝑥 to the power of negative two is one over 𝑥 squared.
In order to answer this question, we need to recall our laws of exponents or indices. Firstly, we recall that 𝑎 to the power of 𝑥 divided by 𝑎 to the power of 𝑦 is equal to 𝑎 to the power of 𝑥 minus 𝑦. If the base value is the same and we are dividing two terms, we can subtract the exponents. This means that our expression can be rewritten as 𝑥 to the power of negative four minus negative two. We know that subtracting negative two is the same as adding two. As negative four plus two is equal to negative two, the expression simplifies to 𝑥 to the power of negative two.
When dealing with negative exponents, we know that 𝑎 to the power of negative 𝑥 is equal to one over 𝑎 to the power of 𝑥. This means that 𝑥 to the power of negative two is the same as one over 𝑥 to the power of two or one over 𝑥 squared. This means that the statement is true. 𝑥 to the power of negative four divided by 𝑥 to the power of negative two is equal to one over 𝑥 squared.
