# Question Video: Evaluating Rational Numbers Raised to a Power Mathematics

Find the value of (β6/5)Β³, giving your answer in its simplest form.

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### Video Transcript

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 π is a positive integer and π over π is a rational number, then π over π to the πth power is equal to π to the πth power divided by π to the πth 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.