Simplify:

Question

5 c left-parenthesis 3 c Superscript 2 Baseline right-parenthesis Superscript 3 Baseline

Answer options with 4 options
A.
45 c Superscript 6 Baseline

B.
135 c Superscript 6 Baseline

C.
45 c Superscript 7 Baseline

D.
135 c Superscript 7 Baseline

Answer 1

To simplify the expression \( 5c(3c^2)^3 \), we can follow these steps:

1. Simplify \( (3c^2)^3 \): \[ (3c^2)^3 = 3^3(c^2)^3 = 27c^6 \]

2. Now we can substitute back into the expression: \[ 5c(3c^2)^3 = 5c(27c^6) \]

3. Multiply the constants and the \( c \) terms: \[ 5 \times 27 = 135 \] \[ c \times c^6 = c^{1+6} = c^7 \]

4. Therefore, the simplified expression is: \[ 135c^7 \]

The correct answer is: D. \( 135c^7 \)