Question

Exponent properties 2c^3m^2 x c^4m simplify

Answer 1

To simplify the expression \( 2c^3m^2 \times c^4m \), we can use the properties of exponents:

1. When multiplying like bases, we add the exponents.
2. We can treat coefficients separately (in this case, the coefficient is 2).

Let's simplify it step by step.

### Step 1: Simplify the coefficients
The coefficient in the first term is 2. The second term does not have a coefficient, which we can consider as 1.

So, the coefficient part is:
\[
2 \times 1 = 2
\]

### Step 2: Simplify the \( c \) terms
For \( c^3 \) and \( c^4 \):
\[
c^3 \times c^4 = c^{3+4} = c^7
\]

### Step 3: Simplify the \( m \) terms
For \( m^2 \) and \( m \):
\[
m^2 \times m^1 = m^{2+1} = m^3
\]

### Step 4: Combine the results
Now, combine all the simplified parts:
\[
2 \times c^7 \times m^3 = 2c^7m^3
\]

### Final Result
Thus, the simplified expression is:
\[
\boxed{2c^7m^3}
\]