To simplify the expression [tex]\( -(5x)^3 \)[/tex], let's break it down step-by-step:
1. Understand the expression inside the parentheses: [tex]\( 5x \)[/tex]. This signifies that both the coefficient [tex]\(5\)[/tex] and the variable [tex]\(x\)[/tex] are to be cubed.
2. Consider the cube operation for the expression [tex]\(5x\)[/tex]:
[tex]\[
(5x)^3 = (5)^3 \cdot (x)^3
\][/tex]
This is because the cube of a product is the product of the cubes of the factors.
3. Simplify [tex]\( (5)^3 \)[/tex]:
[tex]\[
5^3 = 5 \times 5 \times 5 = 125
\][/tex]
4. Also, simplify [tex]\( (x)^3 \)[/tex]:
[tex]\[
x^3
\][/tex]
5. Combine these results:
[tex]\[
(5x)^3 = 125x^3
\][/tex]
6. Now apply the negative sign outside the parentheses to the result:
[tex]\[
-(5x)^3 = -125x^3
\][/tex]
Therefore, the simplified form of the expression [tex]\( -(5x)^3 \)[/tex] is:
[tex]\[
\boxed{-125x^3}
\][/tex]
