Question

Which Expression is equivalent to 144 raised to the three half power expression is equivalent to 144 raised to the three half power

Answer 1

Answer:

$144^{\frac{3}{2} }=1,728$

Step-by-step explanation:

The given expression is

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

We know that every fractional power can be transformed into a root if we use the following property

$x^{\frac{a}{b} } =\sqrt[b]{x^{a} }$

Where $x=144$, $a=3$ and $b=2$, replacing this values we have

$144^{\frac{3}{2} }=\sqrt{144^{3} } =(\sqrt{144} )^{3} =12^{3}= 1,728$

Therefore, the given power is equivalent to 1,728.

Remember that you need to use the right properties to simplify an algebraic expression. In this case we had a power with a fractional exponent, so we applied the property about it.

Answer 2

Answer:

1728

Step-by-step explanation:

We can write the expression as:

$144^{3/2}$ = $12^{2X(3/2)}$

So,

$12^{2X(3/2)}$ = $12^{3}$.

Which is 1728.