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Simplify the following expression completely: [tex]-(5x)^3[/tex].

Enter your answer below without using any parentheses.


Sagot :

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]