High School

Simplify [tex]\((-3x^3)^3\)[/tex].

A. [tex]-9x^6[/tex]

B. [tex]-9x^9[/tex]

C. [tex]-27x^6[/tex]

D. [tex]-27x^9[/tex]

Answer :

We want to simplify the expression

[tex]$$
\left(-3x^3\right)^3.
$$[/tex]

Step 1: Distribute the power to both the constant and the variable expression:

[tex]$$
\left(-3x^3\right)^3 = (-3)^3 \cdot (x^3)^3.
$$[/tex]

Step 2: Compute the power of the constant:

[tex]$$
(-3)^3 = -27.
$$[/tex]

Step 3: Compute the power of the variable by multiplying the exponents:

[tex]$$
(x^3)^3 = x^{3 \times 3} = x^9.
$$[/tex]

Step 4: Combine the results:

[tex]$$
-27 \cdot x^9 = -27 x^9.
$$[/tex]

Thus, the simplified expression is

[tex]$$
-27 x^9,
$$[/tex]

which corresponds to option 4.