### Video Transcript

Which of the following has the same value as negative one and a half cubed divided by negative one and a half squared? Is it A) negative three over two? Is it B) negative 243 over 32? Is it C) three over two, D) negative two over three, or E) two over three or two- thirds?

There are lots of ways of approaching this problem including quite a few shortcuts. If we consider one of the laws of indices, 𝑥 to the power of 𝑎 divided by 𝑥 to the power of 𝑏, this is equal to 𝑥 to the power of 𝑎 minus 𝑏. We can subtract the exponents or indices.

This means that 𝑥 cubed divided by 𝑥 squared is equal to 𝑥. In our example, this means that negative one and a half cubed divided by negative one and a half squared is equal to negative one and a half. We now need to turn this into an improper or top-heavy fraction.

Well one and a half is the same as three halves or three over two. This means that negative one and a half must be equal to negative three halves or negative three over two. Therefore, the option that had the same value as negative one and a half cubed divided by negative one and a half squared was option A), negative three halves or negative three over two.