Indices

NZ Level 6 (NZC) Level 1 (NCEA)

Numerical bases with fractional powers

Lesson

In Powerful Fractions, we learnt about the fractional index rule. Now we are going to apply this rule to terms with numerical bases, so we can evaluate them and get nice, neat answers!

Let's start with a recap of the fractional index rule.

Fractional Index Rule

In general, the fractional index rule states:

$x^{\frac{m}{n}}=\sqrt[n]{x^m}$`x``m``n`=^{n}√`x``m`

Or, if you'd like a more visual representation of this rule, here it is:

When we're evaluating numerical terms with fractional indices, we can solve the root or the power component first. It helps to remember your squared and cubed numbers as it will help you work out which step to do first. One way may give you a nice whole number answer and the other may give you a very long decimal!

Look at the following examples and see how you go at solving these questions.

Evaluate $121^{\frac{1}{2}}$12112.

Express $\sqrt[7]{71}$^{7}√71 in index form.

Question 3

Evaluate $4^{\frac{3}{2}}$432.

Extend powers to include integers and fractions.

Apply numeric reasoning in solving problems