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)

Answer:

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