Use multiplication to expand the expression below. Then compute and/or simplify. (-2xyz) ^ 3
Understand the Problem
The question is asking to use multiplication to expand the expression (-2xyz)^3 and then simplify it. It requires knowledge of exponentiation and multiplication of variables.
Answer
The expanded form of $(-2xyz)^3$ is $-8x^3y^3z^3$.
Answer for screen readers
The expanded form of $(-2xyz)^3$ is $-8x^3y^3z^3$.
Steps to Solve
- Identify the expression to expand
We start with the expression $(-2xyz)^3$.
- Apply the power to the coefficient
The coefficient $-2$ is raised to the power of 3. Calculating this gives: $$ (-2)^3 = -2 \times -2 \times -2 = -8 $$
- Apply the power to each variable
Next, apply the exponent to each variable $x$, $y$, and $z$: $$ (xyz)^3 = x^3 y^3 z^3 $$
- Combine the results
Now combine the coefficient and the variables together: $$(-2xyz)^3 = -8x^3y^3z^3$$
The expanded form of $(-2xyz)^3$ is $-8x^3y^3z^3$.
More Information
When raising a product to an exponent, each factor in the product must be raised to that exponent. This uses the properties of exponents, ensuring each variable and coefficient is treated properly.
Tips
- A common mistake is to forget that you must apply the exponent to each variable separately.
- Another mistake could be miscalculating the power of the coefficient, especially with negative numbers.
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