Questions: The expression a^3 * a^m can be simplified to a^12. What is the value of m? m=

Solution Steps

We are given the expression \(a^{3} \cdot a^{m}\) and need to simplify it to \(a^{12}\). We are asked to find the value of \(m\).

According to the laws of exponents, when multiplying two expressions with the same base, we add the exponents:

\[ a^{3} \cdot a^{m} = a^{3+m} \]

We know that the simplified expression is equal to \(a^{12}\). Therefore, we can set up the equation:

\[ a^{3+m} = a^{12} \]

Since the bases are the same, we can equate the exponents:

\[ 3 + m = 12 \]

Subtract 3 from both sides to solve for \(m\):

\[ m = 12 - 3 = 9 \]

Final Answer