Which expression is equal to [tex][tex]$6(-3m)^4$[/tex][/tex]?

A. [tex][tex]$6(-3)(4) m^4$[/tex][/tex]
B. [tex][tex]$-18 m^4$[/tex][/tex]
C. [tex][tex]$6(-3)^4 m^4$[/tex][/tex]
D. [tex][tex]$6^4(-3)^4 m^4$[/tex][/tex]



Answer :

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]