3p² × p⁴ × 2p⁶
Understand the Problem
The question involves the multiplication of algebraic terms. We will simplify the expression by combining like terms and following the rules of exponents.
Answer
$6p^{12}$
Answer for screen readers
The final answer is $6p^{12}$.
Steps to Solve
- Identify the coefficients and powers of $p$
In the expression $3p^2 \times p^4 \times 2p^6$, we have the coefficients $3$ and $2$, and the powers of $p$ are $2$, $4$, and $6$.
- Multiply the coefficients
We first multiply the coefficients together:
$$ 3 \times 2 = 6 $$
- Combine the powers of $p$
Using the property of exponents that states $a^m \times a^n = a^{m+n}$, we combine the powers of $p$:
$$ p^2 \times p^4 \times p^6 = p^{2 + 4 + 6} $$
- Calculate the total exponent of $p$
Now we sum the exponents:
$$ 2 + 4 + 6 = 12 $$
- Write the final expression
Combining the computed coefficient and the total power of $p$, we write the final expression as:
$$ 6p^{12} $$
The final answer is $6p^{12}$.
More Information
This expression indicates that the product of the algebraic terms results in a coefficient of 6 and a power of 12 for the variable $p$. Such problems often arise in polynomial multiplication, highlighting the importance of both the coefficients and variable powers.
Tips
- Forgetting to add the exponents correctly. Always double-check the addition of powers.
- Mixing up coefficients with powers. Keep them separate to avoid confusion.
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