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 1

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

1. First, we apply the power of a power rule, which states that \((a^m)^n = a^{m \cdot n}\): \[ (4^{-2})^4 = 4^{-2 \cdot 4} = 4^{-8} \]

2. Now, we can rewrite the original expression: \[ 4^4 \times 4^{-8} \]

3. Next, we apply the product of powers rule, which states that \(a^m \times a^n = a^{m+n}\): \[ 4^4 \times 4^{-8} = 4^{4 + (-8)} = 4^{-4} \]

Therefore, the expression \(4^4 \times (4^{-2})^4\) simplifies to: \[ 4^{-4} \]

This is the equivalent expression.