Question

Which of the following would represent the correct process for simplifying the expression below? 242−2=242−2= (1 point) Responses 242−2=24−2=22=4242−2=24−2=22=4the fraction with numerator 2 to the 4th power and denominator 2 to the negative 2 power is equal to 2 raised to the 4 minus 2 power is equal to 2 squared is equal to 4 242−2=24−(−2)=26=64242−2=24−(−2)=26=64the fraction with numerator 2 to the 4th power and denominator 2 to the negative 2 power is equal to 2 raised to the 4 minus negative 2 power is equal to 2 to the 6th power is equal to 64 242−2=24⋅−2=2−8=1256

Answer 1

To simplify the expression \( 2^{4} \div 2^{-2} \), we can use the property of exponents that states \( a^{m} \div a^{n} = a^{m - n} \).

1. Start with the expression: \[ 2^{4} \div 2^{-2} \]

2. Apply the rules of exponents: \[ 2^{4 - (-2)} = 2^{4 + 2} = 2^{6} \]

3. Now, calculate \( 2^{6} \): \[ 2^{6} = 64 \]

The correct representation of the process for simplifying the expression is:

• \( 2^{4} \div 2^{-2} = 2^{4 - (-2)} = 2^{6} = 64 \).

So, the correct answer is that \( 2^{4} \div 2^{-2} = 2^{4 - (-2)} = 2^{6} = 64 \).