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

`144^{(3)/(2) }=1,728`

Explanation:

The given expression is

`144^{(3)/(2) }`

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

`x^{(a)/(b) } =\sqrt[b]{x^(a) }`

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

`144^{(3)/(2) }=\sqrt{144^(3) } =(√(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

1728

Explanation:

We can write the expression as:

`144^(3/2)` =
`12^(2X(3/2))`

So,

`12^(2X(3/2))` =
`12^(3)`.

Which is 1728.