Question

Which expression is equivalent to 144 superscript three-halves?

Answer 1

Using the law of indices the equivalent expression of $144^{\frac{3}{2} }$ is 1728

How to find equivalent expression?

The equivalent expression of $144^{\frac{3}{2} }$ can be express as follows:

Using the law of indices,

$(a^{b} )^{c} = a^{bc}$

Applying this laws,

$144^{\frac{3}{2} }=(12^{2} )^{\frac{3}{2} }$

Hence,

$144^{\frac{3}{2} }=(12^{2} )^{\frac{3}{2} } = 12^{3}$

Finally,

12³ = 1728

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Answer 2

The expression that is equivalent to 144 superscript three-halves ($144^{\frac{3}{2} }$ ) is 1728

Evaluation of expression

From the question, we are to determine the expression which is equivalent to 144 superscript three-halves

The given expression is

$144^{\frac{3}{2} }$

This can be simplified as shown below

$144^{\frac{3}{2} }$

$(12^{2} )^{\frac{3}{2} }$

This becomes

$12^{2 \times \frac{3}{2} }$

$12^{3}$

= 1728

Hence, the expression that is equivalent to 144 superscript three-halves ($144^{\frac{3}{2} }$ ) is 1728.

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