(j) \( \left(m^{3}\right)^{4}=m^{7} \)

Let's first clear the confusion surrounding the expression. To simplify \( \left(m^{3}\right)^{4} \), we can use the power of a power property of exponents, which states that \((a^m)^n = a^{m \cdot n}\). So, by applying this rule, we get: \[ \left(m^{3}\right)^{4} = m^{3 \cdot 4} = m^{12} \] Therefore, the correct equality should be \( (m^{3})^{4} = m^{12} \), not \( m^{7} \). Now let's discuss some common mistakes people make with exponents: A frequent error is adding the exponents when multiplying, instead of multiplying them. Remember, if you see a parenthesis, don’t forget to apply the exponent appropriately!