Question

use the properties of exponents to rewrite the expression. $(-3tu)(-3tu)(-3tu)(-3tu)$
a. $-3t^4u^4$
b. none of these
c. $-(3tu)^4$
d. $(-3tu)^4$

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 \((-3tu)\) is multiplied by itself 4 times: \((-3tu)(-3tu)(-3tu)(-3tu)\).

Step2: Apply the exponent property

Using the property \(a\times a\times\cdots\times a\) (n times) \(=a^n\), where \(a = -3tu\) and \(n = 4\), we get \((-3tu)^4\).

Let's check other options:

• Option A: The coefficient is wrong. The coefficient \(-3\) is also multiplied 4 times, so it should be \((-3)^4\) not \(-3\).
• Option C: The negative sign is outside the base, but our base is \(-3tu\), so this is incorrect.

Answer:

D. \((-3tu)^4\)