Find the value of negative
six-fifths cubed, giving your answer in its simplest form.
We can evaluate the expression in
this question in two ways. Firstly, we recall that negative
six over five cubed can be written as repeated multiplication. It is the product of three lots of
negative six over five as shown. We can then multiply the numerators
and denominators separately, giving us negative six multiplied by negative six
multiplied by negative six over five multiplied by five multiplied by five. Multiplying three negative numbers
gives a negative answer, so the numerator is negative 216. The denominator simplifies to
125. The value of negative six over five
cubed is negative 216 over 125.
We can also evaluate the expression
by recalling the general result for powers of rational numbers. If 𝑛 is a positive integer and 𝑎
over 𝑏 is a rational number, then 𝑎 over 𝑏 to the 𝑛th power is equal to 𝑎 to
the 𝑛th power divided by 𝑏 to the 𝑛th power. This means that we can rewrite
negative six over five cubed as negative six cubed over five cubed, which once again
simplifies to negative 216 over 125.