Question

Simplify:



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. \( 135c^7 \)**