Which expression is equivalent to 144 Superscript three-halves? 216 1,728 RootIndex 3 StartRoot 12 EndRoot RootIndex 3 StartRoot 72 EndRoot

Question:

Which expression is equivalent to 144^(3/2)

1728

Step-by-step explanation:

The options are not well presented. However, this is the solution to the question.

Given:

144^(3/2)

Required:

Find Equivalent.

We start my making use of the following law of logarithm.

A^(m/n) = (A^m)^1/n

So,

144^(3/2) = (144³)^½

Another law of indices is that

A^½ = √A

So,

144^(3/2) = (144³)^½ = √(144³)

144³ can be expanded as 144 * 144 * 144.

This gives

144^(3/2) = √(144 * 144 * 144)

The square root can then be splitted to

144^(3/2) = √144 * √144 * √144

144^(3/2) = 12 * 12 * 12

144^(3/2) = 1728.

Hence, the equivalent of 144^(3/2) is 1728