how to tell the difference between a negative number raised to a power and the opposite of a positive number raised to a power. Use examples in your explanation.
(-n)^p vs -(n^p)
note that if p is even, (-n)^p will be positive, while -(n^p) will always be negative.
Also note that p must be an integer for things to make sense.
yes thank you!
To tell the difference between a negative number raised to a power and the opposite of a positive number raised to a power, we need to understand the rules of exponentiation.
1. Negative number raised to a power: When a negative number is raised to an even power, the result is always positive. But when a negative number is raised to an odd power, the result is always negative.
Example: (-2)² = 4 (positive), (-3)³ = -27 (negative)
2. Opposite of a positive number raised to a power: The opposite of a positive number raised to a power is always negative, regardless of whether the power is even or odd.
Example: -(2)² = -4 (negative), -(3)³ = -27 (negative)
By applying these rules, we can easily distinguish between the two types of exponents.