### Video Transcript

Which of the following has the same
value as one-third cubed divided by one-third squared? Is it A) one-third, B) one-third to
the power of three over two, C) one-ninth to the power of three over two, D)
one-ninth, or E) one to the power of three over two.

As the fractions inside the
brackets or parentheses are the same, we can use one of the laws of indices or
exponents. 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. We can subtract the exponents or
indices. This means that one-third cubed
divided by one-third squared is equal to one-third to the power of one as three
minus two is equal to one.

Any number raised to the power of
one is equal to itself. This means that one-third to the
power of one is equal to one-third. This means that the correct answer
is A.

One-third has the same value as
one-third cubed divided by one-third squared.