Evaluate 25^3/2, Giving Your Answer As A Integer (walk Through)

Question: Evaluate 25^3/2 giving your answer as an integer. (2 marks)

Basic understanding:

Evaluate just means " write this number in a different form/find the answer". In this case the base is the number (25 in the question) and the indices is the power (^3/2 in the question).

First lets establish a² = a x a.

Now, a^1/2 = square-root(a). This is because a power of (^1/2) is finding which number multiplied by itself twice makes the base (a), the literal reciprocal/opposite effect of an integer power of (²) which multiplies the base (a) by itself twice.

Please note you can also have power values of ³, ⁴ , ⁵ etc, or power values of ^1/3, ^1/4, ^1/5 etc. They work in the same way as a power value of ² or ^1/2.

eg: a³ = a x a x a

eg2: a^1/4 = fourth-root(a) [finds which number multiplied by itself four times gives base(a)]

Answer:

Step 1:

Break down the compound indices (power) to two parts, one is the numerator (integer power) and the other is the denominator (fractional power).

eg: 25^3/2 = 25^{3 x 1/2}.

Step 2:

Evaluate (either way) the two separated powers individually. Try priorities the option where you don`t have to work with larger numbers or decimals, the first option in the example below.

eg: 25^1/2 = 5 => 5³ = 125 OR 25³ = 15625 =>15625^1/2 = 125

125 if your final recorded answer.

This is an exemplar walk through so you get an idea on how I tutor. Please do remember this is only one simple way of tutoring this topic and if I had a student to interact with, I would take a different approach if a particular student struggled with any concept. Some students also may struggle learning by reading and are better vocal learners. Either way, I hope this is useful for most students at least.