Question

write the expression using exponents.
(-3)(-3)(-3)(-3)

how should you write (-3)(-3)(-3)(-3) using exponents?
a. -3⁴
b. (-3)³
c. (-3)⁴
d. 4⁻³

Explanation:

Step1: Recall exponent definition

An exponent represents repeated multiplication. For \(a\times a\times\cdots\times a\) (n times), it's \(a^n\).

Step2: Analyze the given expression

The expression \((-3)(-3)(-3)(-3)\) has \(-3\) multiplied 4 times.

Step3: Match with exponent form

So, it should be written as \((-3)^4\). Now check options:

• Option A: \(-3^4\) means \(-(3\times3\times3\times3)\), not the same as 4 multiplications of \(-3\).
• Option B: \((-3)^3\) is \((-3)\times(-3)\times(-3)\), only 3 multiplications.
• Option C: \((-3)^4\) is \((-3)\times(-3)\times(-3)\times(-3)\), which matches.
• Option D: \(4^{-3}=\frac{1}{4^3}\), unrelated to the given expression.

Answer:

C. \((-3)^4\)