(-6x³y)⁴
Understand the Problem
The question is asking us to simplify the expression (-6x³y)⁴. This involves applying the power to each component of the expression, which will require using the exponent rules for multiplication.
Answer
$1296 x^{12} y^4$
Answer for screen readers
The simplified expression is $1296 x^{12} y^4$.
Steps to Solve
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Distributing the Exponent When simplifying the expression $(-6x^3y)^4$, apply the exponent to each component: the coefficient (-6), the variable $x^3$, and the variable $y$.
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Calculating the Coefficient Raise the coefficient to the fourth power: $$ (-6)^4 = 1296 $$
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Calculating the Powers of Variables Raise the variable powers:
- For $x^3$, use the rule $(a^m)^n = a^{m \cdot n}$. Thus, $x^{3 \cdot 4} = x^{12}$.
- For $y^1$, since $y$ has an implicit exponent of 1, we calculate: $y^{1 \cdot 4} = y^4$.
- Combining the Results Combine all the parts to form the simplified expression: $$ 1296 x^{12} y^4 $$
The simplified expression is $1296 x^{12} y^4$.
More Information
This simplification demonstrates how to correctly apply the laws of exponents. Each component of the expression is raised to the power of 4, resulting in an expression that combines both numerical and variable parts.
Tips
- Forgetting to raise the coefficient to the exponent.
- Miscalculating $(-6)^4$. Remember that the negative sign raised to an even exponent results in a positive number.
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