Question

use the properties of exponents to rewrite the expression. $(-4qr)(-4qr)(-4qr)(-4qr)$
a. $-(4qr)^4$
b. $-4q^4r^4$
c. none of these
d. $(-4qr)^4$
reset selection

Explanation:

Step1: Recall exponent property for repeated multiplication

When a term is multiplied by itself \(n\) times, it can be written as the term raised to the power of \(n\). Here, the term \((-4qr)\) is multiplied by itself 4 times.
So, \((-4qr)(-4qr)(-4qr)(-4qr)=(-4qr)^4\)

Step2: Analyze each option

• Option A: \(-(4qr)^4\) has a negative sign outside and the base is \(4qr\) instead of \(-4qr\), so it's incorrect.
• Option B: \(-4q^4r^4\) has a negative sign and the coefficient is \(-4\) instead of \((-4)^4\), so it's incorrect.
• Option D: \((-4qr)^4\) matches the expression we derived from the exponent property.

Answer:

D. \((-4qr)^4\)