Question

simplify: ((3 \times 4)^{2})\\
\\
\\(3 \times 4^{2})\\
\\
\\(3^{2} \times 4^{2})\\
\\
\\(3^{2} + 4^{2})\\
\\
\\(12)

Explanation:

Step1: Apply exponent power rule

The power of a product rule states that \((ab)^n = a^n\times b^n\). So for \((3\times4)^{2}\), we can apply this rule: \((3\times4)^{2}=3^{2}\times4^{2}\)

Step2: Verify other options

• For \(3\times4^{2}\), this is \(3\times16 = 48\), while \((3\times4)^{2}=12^{2}=144\) and \(3^{2}\times4^{2}=9\times16 = 144\), so this is incorrect.
• For \(3^{2}+4^{2}\), this is \(9 + 16=25

eq144\), so this is incorrect.

• For \(12\), \((3\times4)^{2}=12^{2}=144

eq12\), so this is incorrect.

Answer:

\(3^{2}\times4^{2}\) (the second option)