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.
[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.
