Which expression is equivalent to 4, to the power 4 , times, left parenthesis, 4, to the power minus 2 , right parenthesis, to the power 4 , question mark4

4
×(4
−2
)
4
?
Answer
Multiple Choice Answers
4, to the power minus 324
−32

4, to the power minus 34
−3

4, to the power minus 44
−4

4, to the power minus 24
−2

1 answer

To simplify the expression \( 4^4 \times (4^{-2})^4 \), we can use the properties of exponents.

  1. We start with the expression: \[ 4^4 \times (4^{-2})^4 \]

  2. We apply the power of a power property, which states that \( (a^m)^n = a^{mn} \): \[ (4^{-2})^4 = 4^{-2 \times 4} = 4^{-8} \]

  3. Now, our expression becomes: \[ 4^4 \times 4^{-8} \]

  4. Next, we apply the property of exponents that states \( a^m \times a^n = a^{m+n} \): \[ 4^4 \times 4^{-8} = 4^{4 + (-8)} = 4^{-4} \]

Thus, the expression simplifies to \( 4^{-4} \).

Therefore, the correct answer from the multiple choice options is: \[ \boxed{4^{-4}} \]