To determine which expression is equal to [tex]\(6(-3m)^4\)[/tex], we need to interpret and simplify the given expression step by step.
1. First, handle the exponent outside the parentheses:
[tex]\[
6(-3m)^4
\][/tex]
This means we need to raise [tex]\(-3m\)[/tex] to the power of 4.
2. When raising [tex]\(-3m\)[/tex] to the power of 4, both [tex]\(-3\)[/tex] and [tex]\(m\)[/tex] are raised to the power of 4:
[tex]\[
(-3m)^4 = (-3)^4 \cdot m^4
\][/tex]
3. Calculate [tex]\((-3)^4\)[/tex]:
[tex]\[
(-3)^4 = (-3) \cdot (-3) \cdot (-3) \cdot (-3)
\][/tex]
Since multiplying four negative numbers results in a positive number:
[tex]\[
(-3)^4 = 81
\][/tex]
4. Substitute back into the expression:
[tex]\[
6(-3m)^4 = 6 \cdot 81 \cdot m^4
\][/tex]
5. Finally, multiply the constants:
[tex]\[
6 \cdot 81 = 486
\][/tex]
So, the expression simplifies to:
[tex]\[
486m^4
\][/tex]
Thus, the expression that matches this result is:
[tex]\[
6(-3)^4 m^4
\][/tex]
Hence, the correct answer is:
[tex]\[
6(-3)^4 m^4
\][/tex]
