Question

write (-5)(-5)(-5)(-5) as a power.
a) -5⁴
b) (-5)⁴
c) (-1)(5)⁴
d) (-5)×(4)

Explanation:

Step1: Recall the definition of a power

A power \(a^n\) means multiplying \(a\) by itself \(n\) times, where \(a\) is the base and \(n\) is the exponent.

Step2: Identify the base and the number of multiplications

In the expression \((-5)(-5)(-5)(-5)\), the base is \(-5\) and we are multiplying \(-5\) by itself 4 times.
Using the definition of a power, this can be written as \((-5)^4\).

Step3: Analyze the other options

• Option A: \(-5^4\) means \(-(5\times5\times5\times5)\), which is not the same as \((-5)(-5)(-5)(-5)\) because the negative sign is not part of the base being raised to the power.
• Option C: \((-1)(5)^4 = -5^4\), which is the same as Option A and not equal to the given expression.
• Option D: \((-5)\times(4)\) is a multiplication of \(-5\) and 4, not a power representation of the given product.

Answer:

B. \((-5)^4\)