Answer :
To simplify the given expression \((2x)^4\), follow these steps:
1. Understand the expression: We have \((2x)^4\), which means the entire term \(2x\) is raised to the power of 4.
2. Apply the power rule for exponents: According to the power rule, \((a \cdot b)^c = a^c \cdot b^c\). Here, \(a\) is 2 and \(b\) is \(x\), and \(c\) is 4.
Given this, \((2x)^4\) can be rewritten as:
[tex]\[ (2x)^4 = 2^4 \cdot x^4 \][/tex]
3. Calculate \(2^4\): We need to find the value of \(2^4\).
[tex]\[ 2^4 = 16 \][/tex]
4. Combine the results: Now, we multiply \(2^4\) by \(x^4\):
[tex]\[ (2x)^4 = 16 \cdot x^4 \][/tex]
5. Simplified form: Thus, the expression \((2x)^4\) simplifies to:
[tex]\[ 16 x^4 \][/tex]
Therefore, the correct answer is:
D. [tex]\(16 x^4\)[/tex]
1. Understand the expression: We have \((2x)^4\), which means the entire term \(2x\) is raised to the power of 4.
2. Apply the power rule for exponents: According to the power rule, \((a \cdot b)^c = a^c \cdot b^c\). Here, \(a\) is 2 and \(b\) is \(x\), and \(c\) is 4.
Given this, \((2x)^4\) can be rewritten as:
[tex]\[ (2x)^4 = 2^4 \cdot x^4 \][/tex]
3. Calculate \(2^4\): We need to find the value of \(2^4\).
[tex]\[ 2^4 = 16 \][/tex]
4. Combine the results: Now, we multiply \(2^4\) by \(x^4\):
[tex]\[ (2x)^4 = 16 \cdot x^4 \][/tex]
5. Simplified form: Thus, the expression \((2x)^4\) simplifies to:
[tex]\[ 16 x^4 \][/tex]
Therefore, the correct answer is:
D. [tex]\(16 x^4\)[/tex]
