Fully simplify -3x^3(16x^4y^2).
Understand the Problem
The question is asking to fully simplify the expression -3x³(16x⁴y²). This involves multiplying the coefficients and adding the exponents of like bases according to the laws of exponents.
Answer
The fully simplified expression is $-48x^7y^2$.
Answer for screen readers
The fully simplified expression is $-48x^7y^2$.
Steps to Solve
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Multiply the coefficients Multiply the coefficients of the expression. Here, the coefficients are -3 and 16. $$ -3 \times 16 = -48 $$
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Add the exponents of x Next, add the exponents of the like bases. For $x^3$ and $x^4$, we have: $$ 3 + 4 = 7 $$ So, the result for the variable $x$ will be $x^7$.
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Identify the power of y The variable $y$ appears only in the second term with an exponent of 2. Therefore, we keep it as $y^2$.
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Combine all components Now, combine the results from the previous steps to form the final expression: $$ -48x^7y^2 $$
The fully simplified expression is $-48x^7y^2$.
More Information
This expression represents a polynomial where the coefficients and the variables are combined using the rules of multiplication and exponent addition. The resulting expression can be useful in various algebraic contexts.
Tips
- Forgetting to multiply the coefficients correctly.
- Not adding the exponents of the same base properly.
- Disregarding any variables that do not share common bases.
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