What is -5 to the 4 power in expanded form
The Correct Answer and Explanation is :
The correct answer is: 625
To calculate ((-5)^4) in expanded form, we start by expressing the base, (-5), multiplied by itself four times:
[
(-5)^4 = (-5) \times (-5) \times (-5) \times (-5)
]
Now, let’s evaluate this step-by-step.
- First Multiplication:
[
(-5) \times (-5) = 25
]
When multiplying two negative numbers, the result is positive. - Second Multiplication:
[
25 \times (-5) = -125
]
Multiplying a positive number by a negative number gives a negative result. - Third Multiplication:
[
-125 \times (-5) = 625
]
Again, multiplying two negative numbers results in a positive product.
Putting it all together, we have:
[
(-5)^4 = 625
]
Explanation
When calculating a number raised to a power, you multiply the base by itself as many times as indicated by the exponent. In this case, the base is (-5) and the exponent is (4), meaning we multiply (-5) by itself four times.
The key to understanding this operation is recognizing how multiplication of positive and negative numbers works. A negative number multiplied by another negative number results in a positive number, while a positive number multiplied by a negative number results in a negative number. Therefore, when raising (-5) to the fourth power, we first create a positive result by multiplying the first two factors and then alternate between negative and positive results with each multiplication step.
This example also illustrates the concept of even and odd exponents. Any negative base raised to an even power (like (4)) will always yield a positive result, while a negative base raised to an odd power would result in a negative number. Thus, ((-5)^4) results in (625), demonstrating how exponents influence the sign of the product.