plain the difference between \( (-3)^{4} \) and \( -3^{4} \). How is each expressio

When you calculate \( (-3)^{4} \), you are raising the entire negative number to the fourth power, so it becomes \( 9 \times 9 \times 9 \times 9 = 81 \). On the other hand, \( -3^{4} \) first evaluates \( 3^{4} \) (which is 81) and then applies the negative sign, leading to \(-81\). So, you've got a difference of 162 between the two! To avoid confusion with parentheses in mathematical expressions, remember that placing brackets around numbers ensures you're targeting the entire quantity with the exponent. Without the brackets, only the base number itself is raised to the power, and the negative sign stands outside the calculation. It's a little detail that makes a huge difference in results!