Parentheses around Whole Expression vs Leaving out Exponents

Question

What is the difference between:

5 cm^3 

and

(5 cm)^3 

Is there any difference in the sum of this equation? If not, can this be applied to any other equation and result in a change of the answer, or is it just a difference in syntax?

Answer 1

$\left(5\ \mathrm{cm}\right)^3 = 5^3\ \mathrm{cm}^3 = 125\ \mathrm{cm}^3$ is the volume of a cube with a side $5$ centimeters.

$5\ \mathrm{cm}^3$ is a total volume of $5$ cubic centimeters, you need $25$ of those to equate to the previous item

Answer 2

$$(5 cm)^3 = 5^3 cm^3 = 125 cm^3\ne 5cm^3 $$

$(5 cm)^3$ is larger than $5cm^3$ by $25$ times.

$(5 cm)^3$ is the volume of a cube with $5 cm$ on each side.

$5 cm^3$ is the volume of a cuboid with sides $1cm, 1 cm $, and $5 cm$.

Answer 3

$5 cm^3$ vs $(5 cm)^3$: One is five cubic centimeters. The other is 5 centimeters cubed.